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racine carrée 2000-11-24
G. Bigorgne pose la question :
Quel est donc l'origine de l'expression "racine carrée" ? Pourquoi avoir choisi cette expression ?
Claude Tardif lui répond.
Four consecutive positive integers 2019-03-12
Nabila pose la question :
The product of four consecutive positive integers in 24024
What is their sum?

Penny Nom lui répond.
A quadratic equation problem 2019-02-26
Em pose la question :
One root of the equation 2x^2 + bx - 24 = 0 is -8. What are the possible values of b and the other root?
Penny Nom lui répond.
The exponential form of sqrt(13) 2019-02-10
isaebl pose la question :
what is the exponential form of sqrt(13)
Penny Nom lui répond.
Fractions with roots 2019-02-06
DEBMALYA pose la question :
5/√2+√3 –1/√2–√3
Penny Nom lui répond.
The square root 3 in exponential form 2018-05-09
Paige pose la question :
how do you write the square root 3 in exponential form
Penny Nom lui répond.
The square root of 6 is irrational 2017-10-02
John pose la question :
http://mathcentral.uregina.ca/QQ/database/QQ.09.06/sylvia1.html
In the initial assumption of that proof, root 6 is assumed to be a/b where a and b have no common factors, but why does having a common factor make it irrational?

Penny Nom lui répond.
Is the square root of 2 plus the square root of 2 irrational? 2017-03-29
haya pose la question :
how can i prove the the square root of 2 plus the square root of 2 is an irrational number?
Penny Nom lui répond.
Form the quadratic equation which has given roots 2017-01-16
Tharshini pose la question :
Given a and B are the roots of the quadratic equation x^2+4x+7=0. Form the quadratic equation which has the roots 3a-1 and 3B-1
Penny Nom lui répond.
A quadratic equation with equal roots 2016-01-23
abdiwahid pose la question :
X^2+2ax+4x+9a=0 is quadratic equation which has equal roots. Find the possible value of a?
Penny Nom lui répond.
Find the quadratic equation whose roots are -4 and 7 2016-01-03
sadiya pose la question :
Find the quadratic equation whose roots are -4 and 7
Penny Nom lui répond.
The positive root of sin(x) = x^2 2015-12-13
Kemboi pose la question :
Find the positive root of the equation sin(x) = x^2
Penny Nom lui répond.
A quadratic equation with known roots 2015-11-01
Awudu pose la question :
Given the roots of the quadratic equation ax^2+5x+c=0 are 5 and -2/3,find the values of a,b and c.
Penny Nom lui répond.
Square roots 2015-09-21
mariana pose la question :
I have read various articles on how to find the square root of irrational numbers and every article out there seems to be very confusing.
i read you answer to LUKOW about irrational numbers and i am still quite confused. Say i want to find the square root of 326. i know that it is between 18 and 19 because 18 is the square root of 324 and 19 is the square root of 361 im just very confused about the rest of the process. Please help! ( if possible i would appreciate two examples. thanks)

Penny Nom lui répond.
A procedure for finding a square root 2015-08-27
Tracey pose la question :
Is there a method/process to determine the square root of a large number?

For example, Tiananmen Square's area is 396 900m sq., what is the side length?


Thank you,
Tracey

Harley Weston lui répond.
A line segment of length root 5 2014-12-15
angela pose la question :
On the dot grid below, draw and label a line segment with length square root 5 the dot grid is 8 by 10
Penny Nom lui répond.
The cube root of 729 2014-11-12
Alexis pose la question :
What would be the square root of 729 to the third power and could you explain how to get the answer?
Penny Nom lui répond.
Two quadratic polynomials 2014-10-28
khushboo pose la question :
The zeroes of a quadratic polynomial x^2+ax+b are 'c' and 'd' and the zeroes of a quadratic polynomial x^2+cx+d=0 are 'a' and 'b'. find the numerical value of a+b+c+d where a, b, c and d are non zero integers.
Penny Nom lui répond.
1÷[1-√2(order of surd is 4)] 2014-05-02
Anoushka pose la question :
if t=1÷[1-√2(order of surd is 4)] , then t=?
Penny Nom lui répond.
A quadratic equation given the roots 2014-04-23
Sarah pose la question :
How do you find the quadratic formula when you're given just the roots ... X=-3 X= 1/3 Thanks !
Robert Dawson lui répond.
Fractions and square roots 2013-12-04
arionne pose la question :
How do you solve a square root with improper fractions like 121 over 49
Penny Nom lui répond.
Extraneous solutions 2013-10-22
tom pose la question :
i need an equation where x=-2 is the correct answer and x=-3 is an extraneous solution. can you provide me with such an equation??
Harley Weston lui répond.
A quadratic with no real roots 2013-07-15
Pranav pose la question :
If ax^2+bx-5=0 has no real roots. Then d sign of 1) a+b-5 2) (25a-5b-5)(4a+2b-5) will be what ??
Penny Nom lui répond.
Square root 2012-10-27
Ashley pose la question :
what does square root means
Penny Nom lui répond.
Using Newton's Method to find a root 2012-04-09
Nancy pose la question :
Use Newton's method to find the real root function, accurate to five decimal places

f(x) = x^5+2x^2+3

Penny Nom lui répond.
A parabolic arch 2012-01-04
Swathi pose la question :
A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square. The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch is 18m.

a)Determine the quadratic function that models that arch

b)State the domain and range of the function

Penny Nom lui répond.
The square root of z=3+4i 2011-10-27
dianah pose la question :
how to find the square roots of complex number, z=3+4i
Robert Dawson lui répond.
A rational number 2011-05-17
owais pose la question :
according to definition of irrational number "a number which cannot be expressed in p/q form is called irrational number" square root of 2 is a irrational number but if i round off the digit correct to two decimal places so it becomes 1.41 and we can easily convert into p/q form so it is a rational number ???
Penny Nom lui répond.
The quadratic with two given roots and a constant term 2011-04-19
Lindah pose la question :
how do I food quadratic with two given roots and a constant term?
Penny Nom lui répond.
Find all the roots 2010-12-02
gagan pose la question :
find all the roots of z^5-3z^4+2z^3+z^2-3z+2
Stephen La Rocque and Penny Nom lui répond.
z^5 - 3z^4 + 2z^3 + z^2 - 3z + 2 2010-11-06
Kumar pose la question :
would you please solve this problem, related to complex numbers.

Find all the roots of :

z^5 - 3z^4 + 2z^3 + z^2 - 3z + 2

Robert Dawson and Penny Nom lui répond.
A fourth degree polynomial function with real coefficients 2010-10-30
Ryan pose la question :
Question from Ryan, a student: What is the fourth degree polynomial function with real coefficients that has -1,1 and I as zeros and such that f(x)=160
Harley Weston lui répond.
A polynomial with integer coefficients 2010-10-23
Adori pose la question :
Question from Adori, a student: Find a polynomial with integer coefficients that has the given zeros: 2/3, 4, root of 3i, root of -3i.
Harley Weston lui répond.
4√3 + 2√1/3 2010-09-25
Michelle pose la question :
How do you solve 4√3 + 2√1/3? Please show step by step.
Penny Nom lui répond.
Complex roots 2010-04-14
Lan pose la question :
If b and c are real numbers so that the polynomial (x^2) + bx + c has 1 + i as a zero, find b + c.
Penny Nom lui répond.
Rational root theorem 2010-04-14
deciree pose la question :
How could i get the value of x with this equation: 1/13x^3+12x/13=1/2 Thank you!
Harley Weston lui répond.
Factors and zeros of a polynoial 2010-03-17
Susan pose la question :
find a polynomial function of degree three with -3 as a zero of multiplicity 2 and 4 as a zero of multiplicity 1.
Tyler Wood lui répond.
Zeros of a polynomial 2010-03-01
Gavin pose la question :
Suppose the polynomial R(x) = a_9x^9+a_8x^8+...+a_1x+a_0 has real coefficients with a_9≠0. Suppose also that R(x) has the following zeros:
2,
3,
i

Using this info, answer the following.

a. What is another zero of R(x)?
b. At most how many real zeros of R(x) are there?
c. At most how many imaginary zeros of R(x) are there?

p.s. I used _ for subscript
thanks so much

Harley Weston lui répond.
The roots of a cubic 2010-01-21
Laura pose la question :
Consider the equation x^3 + 6x^2 - x = 30. One of the roots is equal to the sum of the other two roots. Find the values of the three roots.
Chris Fisher and Harley Weston lui répond.
The square root of a large number 2010-01-19
darlene pose la question :
I understand the simple process, like 12 is the root to 144 but what happens when the number is 42563. Without a calculator how does a person figure this out during a timed test?
Robert Dawson lui répond.
Figure out the square root of something 2009-12-20
eric pose la question :
is there an ez equation to figure out the square root of something?
Harley Weston lui répond.
Excluded values 2009-11-14
Janie pose la question :
I have to State the excluded values for this equation and then solve, but not sure how to do this. Here is the problem
(x+6)/x+3=(3)/(x+3)+2

Harley Weston lui répond.
The roots of a polynomial 2009-11-03
Jess pose la question :
Find the value of a positive integer k such that f(x)=x^2 - 2kx + 55 has roots at k +3 and k - 3.
Penny Nom lui répond.
Rationals 2009-10-30
Jawsh pose la question :
I don't quite understand the whole idea of rationals. If you have 3Squareroot 49. Is that equal to 3Squareroot 7^2? Can you break it down with an example for me please.
Robert Dawson lui répond.
The zeros of a polynomial 2009-09-25
jordan pose la question :
find a polynomial of lowest degree with only real coefficients and having the given zeros. 1+2i, 2 (multiplicity 2)
Penny Nom lui répond.
Quadratic equations 2009-08-30
jovian pose la question :
how can i find the quadratic equation of the roots 2/5 and -1/3?
Stephen La Rocque lui répond.
root 2 is irrational 2009-07-31
prateet pose la question :
prove that root2 is an irrational number.
Robert Dawson lui répond.
Inequalities Proof 2009-07-24
ABOU pose la question :
good morning.......a b c are real positive no zero......proof that sq root(2a/(a+b))+sq root(2b/(b+c))+sq root(2c/(c+a))inferior or equal 3 thank you
Janice Cotcher lui répond.
Fractional Exponents 2009-07-07
bob pose la question :
2^5/2 - 2^3/2
Janice Cotcher lui répond.
Extraneous solutions 2009-06-02
Ayana pose la question :
solve and check for extraneous solutions.

3x+6/ x²-4 = x+1/ x-2

x can not = {-2,2}

Penny Nom lui répond.
How many times does the graph of y=2xsquared -2x + 3 intersect the x-axis? 2009-05-27
Henry pose la question :
how many times does the graph of y=2xsquared -2x + 3 intersect the x-axis?
Penny Nom lui répond.
A quadratic equation with roots (4-i) and (4+i) 2009-05-05
Kelly pose la question :
find a quadratic equation with roots (4-i) and (4+i)
Harley Weston lui répond.
1/(square root 16) 2009-04-21
Conor pose la question :
Hi Guys!

I dont have a square root sign so im just gonna use the ^ symbol :)

I am just wondering if

1/(16^a)

when re-written can it be

1/16 to the power -1/2

Thanks :)

Penny Nom lui répond.
The sum of the roots of a quartic 2009-04-21
dave pose la question :
This is a algebra problem that i am confused about: The sum of the roots of x^4-x^3+5x^2+4=0 is: i tried graphing it, but it shows that there are no roots, but the answer is 1. are they wrong?
Penny Nom lui répond.
More on the square root of 0.75 2009-03-30
Blaine pose la question :
I read your response to How is the square root of 3/4 is greater than 3/4?

What I'm hoping for is a way for my students to use their own experience and number intuition to be able to make sense of the issue. As soon as my kids see "if y is this and x is this then..." their little eyes glaze over. Unfortunately, I can't come up with a way myself. Thank you for your help.
Penny Nom and stephen La Rocque lui répond.

Find a polynomial function with the indicated zeros and satisfying the given conditions 2009-03-23
Kristen pose la question :
Find a polynomial function with the indicated zeros and satisfying the given conditions. Simplofy your answer (no imaginary numbers or parentheses in the answer) Zeros: 1+2i, 1-2i, 5 ; f(-2)=1
Harley Weston lui répond.
Simplify the square root of 125 x^2 2009-02-27
Ashley pose la question :
√125x²

How do you simplify this equation assuming that variables can represent any real number?

Robert Dawson lui répond.
ax^2 + bx + c = 0 has no real roots and.... 2009-01-26
Alberto pose la question :
The equation ax^2 + bx + c = 0 has no real roots and a + b + c < 0 . Chose the right answer:

(A) c > 0
(B) c <= 0
(C) c = 0
(D) c >= 0
(E) c < 0
Explain the choice.

Robert Dawson and Harley Weston lui répond.
The sum of the roots of a quartic 2009-01-03
peter pose la question :
How do you find the roots of an equation without graphing? like, i have a problem that says what is the sum of the roots of x^4-x^3+5x^2+4=0.
Harley Weston lui répond.
The square root of 164 2008-12-31
Melissa pose la question :
How do you simplify the square root of 164?
Stephen La Rocque lui répond.
Factor 9x^2 + 6x + 4 2008-11-21
Jonah pose la question :
how can i solve this by factoring: 9x^2 + 6x + 4
Harley Weston lui répond.
An equation with three radicals 2008-11-13
Crystal pose la question :
I need to solve this radical equation but i am confused on how to solve it with three square roots in it. sqrt(3x)+3-sqrt(2x-3)=sqrt(3x-2)
Harley Weston lui répond.
Equations with fractional powers and roots 2008-11-12
David pose la question :
Find all real solution to each equation.

x^-2/3 = 9 how do you do this if its to the power

x + 1= Square root (3x +13) can you explain how to get an solution with square root?

Penny Nom lui répond.
Solving an Equation with a Square Root 2008-10-05
Jonathan pose la question :
the square root of 3x+18 = x 3x+18 are within the square root
Victoria West lui répond.
The square root of a fraction 2008-08-24
Lauren pose la question :
How do you solve square roots of fractions? Does the format change if it is either a proper or an improper fraction?

Ex. the square root of 1/4 or the square roots of 80/25

Penny Nom lui répond.
The cube root of a really big number 2008-07-17
Pete pose la question :
Is the only way to find a cube root of a really big number guess and check, as i read in other questions, or is there another way without a calculator?
Harley Weston lui répond.
Sum and product of the roots of a quadratic 2008-07-03
Gautam pose la question :
If a and b are the roots of x^2+px+1=0 and c and d are the roots of x^2+qx+1=0
prove that
(a-c)(b-c)(a+d)(b+d)=q^2-p^2
Regards
Gautam

Harley Weston lui répond.
The square root of (18*n*34) 2008-07-01
Peter pose la question :
What is the least possible positive integer-value of n such that square root(18*n*34) is an integer?
Penny Nom lui répond.
The positive real zeros of f(x) = x^4 + x^3 - 7x - 1 2008-06-06
CiCi pose la question :
How many positive real zeros does the function f(x) = x4 + x3 - 7x - 1 have?
Janice Cotcher and Harley Weston lui répond.
A quadratic equation 2008-06-03
Drew pose la question :
A solution of x^2-8x=-17 is

-4 or -4+I or 4 or 4+i

Janice Cotcher lui répond.
A root of a polynomial 2008-05-03
john pose la question :
here is a word problem that my teacher gave us to do can you help me understand it

Give possible formulas (in factored form) and sketch the graphs for two different polynomials that have roots -3, -1, and 2, but cross the x-axis only at x=2 and have y-intercept 4.5. What is the lowest degree such a polynomial can have? Can it have an even degree? An odd degree? Explain why.

her term "root" has completely thrown me off, i've reviewed my book and cant find what she is referring to. can anyone help?

Penny Nom lui répond.
For what values of a does x^3-13x+a have 3 distinct roots? 2008-04-25
Jyotishman pose la question :
What can be the value of a for the equation to have 3 roots?
x^3-13x+a=0

Harley Weston lui répond.
How is the square root of 3/4 is greater than 3/4? 2008-04-22
Serena pose la question :
How is the square root of 3/4 is greater than 3/4?
Penny Nom lui répond.
Find the quadratic equation with roots at (3-i) and its complex conjugate 2008-04-22
Tiffany pose la question :
Find the quadratic equation with roots at (3-i) and its complex conjugate.
Penny Nom lui répond.
The square root of 21 between what two numbers? 2008-04-03
Danielle pose la question :
The square root of 21 between what two numbers?
Penny Nom lui répond.
The cube root of 198 2008-03-27
bobby pose la question :
what is the cubed root of 198
Harley Weston lui répond.
The product of the roots 2008-03-19
Rebecca pose la question :
Determine the product of the roots of the equation (x-1)(x-2) + (x-2)(x-5)=0
Penny Nom lui répond.
The sum and product of the roots of a quadratic 2008-03-16
Katelyn pose la question :
Write the quadratic equation....

Sum of the roots = 16
Product of the roots = -80

Penny Nom lui répond.
Estimate the cube root of 270 2008-03-11
Tom pose la question :
(a) By plotting suitable graphs, estimate to one decimal place the cube root of 270.
(b) With reference to your answer to part (a), use 8 iterations of a Bisection Search to refine your estimate. Use the nearest whole numbers either side of your estimate from part (a) as starting values.
(c) Using either of your starting values from part (b) as first guess, use the Newton-Raphson method to find the true value of the root (to 6 decimal places). Repeat using the other starting value from part (b) and compare the two results.

Harley Weston lui répond.
The cube root of 103163 2008-02-12
jeff pose la question :
find the cube root of 103163
Stephen La Rocque and Harley Weston lui répond.
Graphing a parabola 2008-01-16
Sean pose la question :
How do I find the roots and describe the roots when graphing a parabola?

y = - x^2 - 4x -3

Stephen La Rocque lui répond.
Simplifying square roots 2007-12-19
Ciara pose la question :
How would you calculate 2 to the square root of 8 plus 4 to the square root of 2 minus 5 to the square root of 2?
Stephen La Rocque lui répond.
The rational root theorem 2007-12-09
Josh pose la question :
Prove the rational root theorem (where, in a polynomial equation, all factors of the constant divided by all factors of the leading coefficient are possible rational roots of the equation).
Penny Nom lui répond.
Imaginary roots 2007-12-09
Josh pose la question :
What is the correlation between imaginary roots (of a quadratic or other polynomial equation) and the graph of the equation? As in, how can one represent imaginary solutions graphically (and why does that work)?
Harley Weston lui répond.
1-4/square root 3 2007-09-12
Prudence pose la question :
How to solve this question?
1 - 4/√3

Penny Nom lui répond.
Does every number have a square root? 2007-09-10
Cheryl pose la question :
Does every number have a square root?
Harley Weston lui répond.
Simplify (square root of)200 2007-08-28
melissa pose la question :
how do you simplify: (square root of)200
Penny Nom lui répond.
What feature on a graph shows the solution? 2007-08-19
San pose la question :
To solve the equation 2sinx+square root 3=0, what feature of the graph, in the form y=asinx+b would show the solution? Draw a graph to show the solution. thanks.
Stephen La Rocque lui répond.
The roots of (x - k)(1-3x) + 1 = 0 2007-06-28
Claire pose la question :
Show that the roots of (x - k)(1-3x) + 1=0 are real and distinct for all real values of k. Hence, or otherwise, find the range of 9sin^2 r - 6sin r + 13
Harley Weston lui répond.
Simplifying a square root 2007-05-24
Leigh pose la question :
I am trying to help my son. Simplify sq root 81 x to the 2nd power y to the 12th power.
Stephen La Rocque lui répond.
Finding the equation given three roots 2007-05-21
Aydee pose la question :
1. find the equation for the roots given: 7,-5,2
2. find the equation for the roots given: -5,2+sqrt3,2-sqrt3

Penny Nom and Stephen La Rocque lui répond.
Finding square roots 2007-05-17
Chandler pose la question :
I would like an easy way to find the square root of a number.
Gabriel Potter lui répond.
What is the square root of 729 to the third power? 2007-04-25
Tori pose la question :
What is the square root of 729 to the third power?
Penny Nom lui répond.
x^3 - 3kx + 1 = 0 2007-03-11
Sandra pose la question :
Show that x^3 - 3kx + 1 = 0 does not have two distinct roots when k < 0.
Stephen La Rocque and Penny Nom lui répond.
Finding the x-intercept 2007-03-02
Ash pose la question :
Y = -1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT
Gabriel Potter lui répond.
The cube root of 8000 2007-01-31
Jacqui pose la question :
How would you find the answer of a cube root backwards. For example: 8000 but backwards. Like, what number made that and how would you do it?
Penny Nom lui répond.
5sqrt2+3 2007-01-07
Mike pose la question :
I don't understand why 5sqrt2+3 is the correct answer over 5sqrt 5
Penny Nom lui répond.
Prove that square root of 3 is irrational. 2006-12-21
Humera pose la question :
Prove that square root of 3 is irrational.
Stephen La Rocque lui répond.
The roots of a quadratic equation 2006-11-16
Lana pose la question :
If p and q are the roots of 2X^2 +3X+7=0, compute pq^3+qp^3. thanks for your help.
Penny Nom lui répond.
Help me prove that the square root of 6 is irrational 2006-09-23
Sylvia pose la question :
Could you please help me prove that the square root of 6 is irrational ?
Stephen La Rocque lui répond.
Is this unsolvable? 2006-09-19
Al pose la question :
Is this unsolvable???

2xy + 3x^2 - 3y + y^3 = 4x + 3 where y=3.
Penny Nom and Claude Tardif lui répond.

Square roots in a binomial expansion 2006-09-11
Sydney pose la question :
(√x + 5)4 expanded using the binomial theorem
Penny Nom lui répond.
The square root of 4 2006-05-07
MaryBeth pose la question :
I am a high school teacher of Algebra. I was recently teaching square roots to my students and an interesting question arose. Our textbook seems to be inconsistent. I was hoping you might be able to give our department your opinion on who is correct as we are divided on the correct way to teach this. When you take the square root of a number, you get two answers, a positive root and a negative root, correct? Our book presents this as √4 = 2 and -√4 = -2 and ±√4 = ±2. Shouldn't it be taught as there are always two roots, the positive and the negative? It seems to me, there is really no reason to have to use the ± as there are always 2 roots, the positive and the negative. But if the negative sign is given then only the negative answer should be given? What's your take?
Penny Nom lui répond.
Finding square roots 2006-04-12
Fehmida pose la question :
I would like to know about tricks or formulas to do complicated square roots. ex. square root of 1029
Penny Nom and Steve La Rocque lui répond.
Square roots 2006-03-07
Diana pose la question :
Find each square root
Harley Weston lui répond.
The square root of i 2005-11-30
Kevin pose la question :

If the square root of -1 is i, what is the square root of i?

How can you find the log of a negative number?

What is the log of -1?


Claude Tardif lui répond.
Quadratic Equations & Given Roots 2005-11-11
Lindsey pose la question :

I need to find the quadratic equation in the form:
f(x)=a(x2 - (-b/a)x + (c/a))

The vertex is (1, -7), the roots are (4, ?)

I need to find the other root but I don't know where to begin. My answer key says the other root is (-2). How is this possible?


Penny Nom lui répond.
|ax+b| = cx + d 2005-03-22
Angel pose la question :

|ax+b| = cx + d

how to show sometimes the above has 2 roots, sometimes 1 root and sometimes no roots. Hopelessly lost on how to start...


Penny Nom lui répond.
The square root of 2 2005-03-12
Madhumita pose la question :
From Pythagoras theorem we can draw square root 2 as a finite distance but it is irrational number which is endless. Explain how we can equate these two.
Harley Weston lui répond.
Factoring a cubic 2005-02-20
Abraham pose la question :
How would you factor completely,
x3-x2+5x-5?

Claude Tardif lui répond.
Solve for x 2005-02-02
Christie pose la question :
Solve for x

.387 = (.40 - .265x)/(sqrt(1-x2))

Penny Nom lui répond.
Imaginary roots of a ploynomial 2004-10-31
Jennifer pose la question :
how to find the roots of a polynomial equation if it would be imaginary?
Harley Weston lui répond.
Cube roots 2004-10-26
A parent pose la question :
How do you solve the problem of finding the cubed root of (17 to the power of 3).
Can you show me each step and if you have a visual representation of this it would be very helpful.

Also can you show a step by step of finding the cubed root of 27. Visuals help a lot

Penny Nom lui répond.
Square roots and inequalities 2004-10-25
Waheed pose la question :
Q1. What is the simplest way of finding a square root of any number using just a pen and paper? (I am asking this question because I browsed a few sites a didn't find any method that is simpler than the one I use. so I am just curious.)

Q2. Is it possible that you take an equation and turn it into an inequality by performing same mathematical operations on both sides?

Claude Tardif and Penny Nom lui répond.
The distance formula 2004-09-04
Joe pose la question :
Why do we use square roots and squares in the distance formula Wholdnt they cancel each other out?
Claude Tardif lui répond.
square root 125 x 16 2004-04-23
Mike pose la question :
how do you simplify a square root of "- square root 125 x16" when x is a variable... i don't really get how to do this....
Penny Nom lui répond.
Even-numbered roots 2004-03-01
A student pose la question :
I understand that the square root is defined to be positive only. Does the same rule apply to other even-numbered roots, such as the 4th root, or the 6th root, etc.?
Harley Weston lui répond.
root24 = 2 root6 2003-11-13
Burke pose la question :
I know that all algerbra can be represented visually, for example: Y=9x+3 is a line on a two dimentional plane. Could Math Central please send me a visual representation of the proccess of simplifying square root like root24 equals 2root6
Penny Nom lui répond.
Polynomials degree 4 and bigger 2003-06-26
Stephen pose la question :

How do I show kids how to find all the zeros for polynomials degree 4 and bigger.

For examples:
r(x) = x5-11x3-7x2+77 = (x2-11)(x3-7) and s(x) = x4-121 = (x2-11)(x2+11)

Also am I correct when I say that the following are irreducible?

f(x) = x2-11
g(x) = x3-7
h(x) = x4-5


Harley Weston lui répond.
2/sqrt(2) 2003-05-07
Mike pose la question :
I was looking at an example of csc 45 deg where

csc = hyp / opp = 1 / (sqrt(2) / 2) = 2 / sqrt(2) = sqrt(2)

I just don't get this. If sqrt(2) = 1.4142145..... How can 2 / sqrt(2) = sqrt(2) as the example shows?


Penny Nom lui répond.
Can twice a square be a square? 2003-03-25
Mike pose la question :
The other day it occurred to some students that they could think of no square number which is an integer, which can be divided into two equal square numbers which are intergers, Or put another way, no squared integer when doubled can equal another square integer. For example 5 squared plus 5 squared is 50, but 50 is not a square number.
Walter Whiteley and Claude Tardif lui répond.
Extraneous solutions 2003-01-24
Paul pose la question :

What is an extraneous solution and in what cases do you get one?

How do you know it is extraneous?


Penny Nom lui répond.
Quadratic equations 2002-12-10
Katie pose la question :
just bugging the hell outta me and I cannot figure it out for the life of me.

1)x-2x-1 =0
Find both roots. You must simplify both of your roots. This equation requires the use of the Quadratic Formula. I have tried everything for this and I am still either getting the wrong answers, and end up getting really frustrated. If you could find the answers and tell me how you did it I would greatly appreciate it! Then the second problem is

2) The square of a certain negative number is equal to 70 decreased by 3 times the number. Find the answer! On this one I set it up but still came out with the wrong answer. So if you could help me on this one I would greatly appreciate it!

Penny Nom lui répond.
Factoring a cubic 2002-12-05
Dorota pose la question :
I got a problem with factorise the expression
2x3+11x2-5x-50.

Penny Nom lui répond.
Constructing the square root of 3 2002-06-07
Allan pose la question :
I am a Math 7/8 teacher. I was wondering how you would show a student how to find the exact location of the square root of three on the number line using just a compass and a straight edge.
Penny Nom lui répond.
A polynomial 2002-04-14
A student pose la question :
A polynomial function is described by the following conditions: f(x) has two real zeros at x= -2 and x= 1, each of multiplicity 2 f(x) has two complex zeros as x goes to -infinity, f(x) goes to +infinity as x goes to +infinity, f(x) goes to +infinity f(x) has a y-intercept at (0,2)

Sketch a polynomial function that satisfies the above conditions.

Write an equation for function f(x)

Write another function g(x) that also satisfies the above parameters.


Penny Nom lui répond.
The square root of four 2002-04-13
Frank pose la question :
In a recent quiz we where asked the square root of four. The quizmaster gave the answer as not only 2 but also -2. Being pedantic I queried this. Although -2 squared is 4, does it follow that the root of 4 is -2 Can you enlighten us?
Claude Tardif and Penny Nom lui répond.
Cube roots 2002-03-26
Kathy pose la question :
My son is in 4th grade and needs to simplify the cube roots of 216, 512 and 64. How does he do this with a regular calculator or without?
Penny Nom lui répond.
The square root of i 2002-03-14
Arlene pose la question :
what is the square root of i, if i=x+yi?

what is the square root of 1-i? i'm getting problems like these in which I do not understand.


Harley Weston lui répond.
The square root of 2 2002-03-05
Roger pose la question :
Does two (2) have a square root or do the numbers just keep going? Are there any other numbers that behave like two when it comes to extracting the square root?
Penny Nom lui répond.
Double square roots 2002-02-17
Ali pose la question :
i have a question about how to do double square roots with variables and powers.

example : v/"" v/"" 81y8


Harley Weston lui répond.
A degree 5 polynomial 2002-02-17
Carla pose la question :
Write an equation for a polynomial of degree 5 given the following zeros:
-7+3i, -2+sqrt(13), 6

Penny Nom lui répond.
2=the square root of (2 + the square root of (2 + the square root of (2 +...))) 2001-11-05
Cynthia pose la question :
justify algebreically, that:

2=the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + and so on, .......


Penny Nom lui répond.
Squares of negative numbers 2001-11-03
Susana pose la question :
I wanted to know if I can square a negative number..?
Leeanne Boehm lui répond.
The square root of 20 2001-09-18
Dianna pose la question :
How do you simplify a square root? My daughter tells me that the square root of 20 simplified is 5root4
Penny Nom lui répond.
The square root of 21/168 2001-09-10
A student pose la question :
can you show me how to do this square root of 21/168
Penny Nom lui répond.
Some irrational numbers 2001-07-03
Kellie pose la question :
  1. Is it possible to write pi as a fraction?

  2. Is it possible to write the square root of 2 as a fraction.. Explain why?

Harley Weston lui répond.
Primes and square roots 2001-06-14
Paul pose la question :
I have a bit of a math problem. It has to do with determining if a very large number is a prime. One method entails dividing the number by every smaller prime number. If any divide into it, it's not a prime. This would be a big job if the number was something like 400 digits long. Another way I read about was to take the square root of the number and test all the primes less than its square root. The explanation went like this: "When a number is divided by another number that is greater than its square root, the result is a number smaller than the square root. For example, the square root of 36 is 6. Dividing 36 by 2, a smaller number than 6, gives 18, a number that is larger than the square root. To prove that 37 is prime it is only necessary to divide it by primes less than 6, since if it had a prime factor greater than 6, it would have to have one less than 6 as well."

I understand the explanation, up to the last sentence. I fail to see the underlying logic. Why if a prime factor exists below the square does one have to exist above the square too? The number 40 can be divided by the prime 2, a number below its square root, but no other primes can do this above its square root. Have I missed something? What's the logic here?


Claude Tardif and Penny Nom lui répond.
25 y^2 + 20 y z - 4 z^2 2001-05-15
Kimmy pose la question :
i don't know how to factor the trinomial 25y2 + 20yz - 4z2. I can get it, but i get messed up on getting the minus 4 at the end. all i get is a plus 4. Can it even be factored.
Penny Nom lui répond.
Teaching square roots 2001-05-08
Katie pose la question :
My friend and I are doing a project. We have to teach our class about square roots. What is the easiest way to teach square roots to a class?
Penny Nom lui répond.
Cube roots on a calculator 2001-03-24
Will pose la question :
Hi my name is Will.I have a question about the calculator TI-83 Plus or the use of a scientific calculator. It is about using them to turn a cubed root to a decimal. When using that for a rational and irrational number. Rational numbers is a number that terminates or repeates. A irrational number goes on and on and uses ... (like pie). Like when you type the cube root of 8 it gives you 2, and that is a rational number. The squre root of 2 is 1.41421356... that is irrational. So why is it when you put the cube root of 16 in the calculator it says 2.5198421 that is rational it terminates at the ninth digit and my float is set for the tenth? But why when you do it by hand you get the 2 times the cube root of 2 and that is irrational? Why is that?
Judi McDonald lui répond.
Radicals 2001-03-18
Nikki pose la question :
3) squareroot of x2 + 10x + 25

4) sixthroot of (m + 4)6

5) cuberoot of -64r6w15

.
.
.
.

Penny Nom lui répond.
Finding roots 2001-02-01
A student pose la question :
My math problem is right now we are working on roots. I don't quite understand how to find the answer to the problems, i was wondering what is the easiest, and fastest way to find the answers to roots?
Penny Nom and Claude Tardif lui répond.
The solutions of a quadratic 2001-01-30
A student pose la question :
  1. Show that the product of the solutions of ax2 + bx + c = 0 is c/a.

  2. For each equation under the given condition, (a) find k and
    (b) find the other solution.
    kx2 - 2x + k = 0; one solution is -3

Penny Nom lui répond.
Some complex problems 2001-01-15
Nick pose la question :
I am having enormous difficulty with one question in my maths homework. The question is shown below. If anybody out there can find the answers and show the workings and help me to understand.
Harley Weston lui répond.
Completing the square 2001-01-12
Jacky Lam pose la question :
A friend told me that completing square not only can find the vertex but also the roots of a quadratic equation. Is it possible? How? Can you show me how to find the roots of the following equation using completing the square?

8x2 + 8x + 4


Penny Nom lui répond.
An infinite series 2000-12-16
John pose la question :
summation(n=1 to infinity)[n sin(1/(2n))]n
Harley Weston lui répond.
Square roots 2000-10-29
Pamela pose la question :
HERE GOES(I WILL USE Q AS THE SYMBOL FOR SQUARE ROOT):

8(Q2) - 5(Q2) + Q2

SECOND PROBELM IS

(1 + Q2)2

LAST ONE

3/(2-Q5)


Claude Tardif lui répond.
Roots of x^2 + 22 x + 112 2000-09-07
Brian R. pose la question :
I need to find the root of the quadratic equation of a square. The problem is x2 + 22x + 112 = 0.
Penny Nom lui répond.
A equation with a square root 2000-09-03
Lea pose la question :
Please help with 2 plus the square root ( and under it has x plus 1) = 6
Thank you

Penny Nom lui répond.
The square root of -1 2000-05-19
Gary pose la question :
i am not a student i am just some one that heard something and i can't be sure on the answer...my ? is what is the square root of -1? i think it is -1 but not sure can you let me know please thank you
Harley Weston lui répond.
Graphing cube roots 2000-04-27
Heather Jones pose la question :
What do the graphs of cube roots look like?
Walter Whiteley lui répond.
Finding a Quadratic Equation given the roots 2000-04-16
A secondary student pose la question :
How do I find the equation for the quadratic with roots at 2-i and its complex conjugate?
Harley Weston lui répond.
All the roots of x^6 - 64 2000-04-15
Dakota pose la question :
Find ALL zeros of P(x) = x 6 - 64
Walter Whiteley lui répond.
The square root of 3 2000-04-04
Mr. William pose la question :
Prove that root 3 is irrational
Harley Weston lui répond.
root(-1)* root(-1) 2000-03-20
Michael Moran pose la question :
i squared = -1

but

i squared = root(-1)* root(-1)
= root( -1*-1)
= root(1)
= 1
-1 doesn't = 1

can you help me with my question


Claude Tardif lui répond.
Irrational algebraic functions 2000-02-21
Bucky Cadena pose la question :
Here is the multipart problem:

Given f(x) = x-3* squareroot of x + 4

What does the f(x) intercept equal Find the two values for which f(x) = -5 Find the one value for which f(x) = -3


Harley Weston lui répond.
Complex Roots 2000-01-24
Jess Rutherford pose la question :
How do I find the value of k when 5x2 + k = 3x and has complex roots ?
Penny Nom lui répond.
Calculating a square root 1999-10-28
Jonathan pose la question :
What is the formula for calculating a square root?
Penny Nom lui répond.
Square roots without a calculator 1999-09-14
Josh Weiner pose la question :
Is there any way to find out a square root without a calculator?
Harley Weston lui répond.
Spreading a rumor 1999-09-13
Bornstar14 pose la question :
There is someone who wants to spread a rumor within 7 days to 250,000,000 people. he wants to know how many people he should tell on the first day (assuming the rumor is passed by everyone who was told to the same amount of people) so that everyone knows on the 7th day. What I did is the 7th root of 250,000,000. this answer is not possible unless rounded. is it okay for the number to be approximate?
Penny Nom lui répond.
The square root of two is never supposed to end 1999-03-06
a wondering student pose la question :
i am algebra II and am in the 9th grade. today we were talking about rational and irrational numbers. When we were talking about square roots my friend and i were talking and we thought of something. if you have a square with sides of length one then the diagonal of the square is the square root of 2. Now the square root of two is never supposed to end. But the diagonal of the square ends so therefore doesn't the square root of 2 end. our math teacher did not really answer our question because it was not in the lesson plan and not to many people would see where we were coming from. the answer is really bugging me and i would like to have your input.
Jack LeSage and Penny Nom lui répond.
Simplifying Radicals 1999-01-26
Mary pose la question :
I would like to know how to simplify this question:
   
4 __________________ squareroot7 + squareroot3 
I know the answer is (sqrt7 - sqrt3) but i would really love to know how to get that answer!! Thanks.

Jack LeSage and Penny Nom lui répond.
Simplifying Radicals 1999-01-25
Randy pose la question :
Find the perimeter of a rectangle in simplified radical form L=root80 W=root45. I would appreciate a detailed explination of the process for solving.
Jack LeSage and Penny Nom lui répond.
Root 17 is Irrational 1999-01-21
John Murdock pose la question :
If you could help me out with this I would appreciate it. Prove that the square root of 17 is irrational.
Harley Weston lui répond.
Complex Numbers 1998-12-23
Wayne Bagley pose la question :
I would like to know what is the square root of i , and i squared? I am looking for a response appropriate for secondary level students.
Harley Weston lui répond.
Simplifying Roots 1998-09-18
Lauren Lattimer pose la question :
1. 2root27 divided by root 12

2. 3 root 48-root 75
Penny Nom lui répond.

Radicals 1998-09-15
Lana Sabo pose la question :
Question:
fifteen times the square root of twenty, divided by the square root of 2.

nine subtract the square root of forty-five, divided by 3.

the square root of 18 plus the square root of 12, divided by the square root of 3.
Harley Weston lui répond.

The Factor Theorem 1998-01-18
Dhruv Bansal pose la question :
Hi, I'm a ninth grade student doing a math project for school. I'm trying to learn about various ways of solving 3rd and 4th degree polynomial equations using the remainder theorem, the factor theorem, and synthetic division. The books I have all mention x - r, which I know nothing about, not even how to get it.

I would really appreciate any information on this. Thanks.

Dhruv Bansal
Penny Nom lui répond.

Multiplying imaginary numbers. 1997-11-03
Jim Catton pose la question :
Here is the question:

(square root -2) x (square root -8)

My algebra suggests two possibilities .
.
.

Walter Whiteley, Chris Fisfer and Harley Weston lui répond.

The Range of a Function. 1997-09-12
Karel Marek pose la question :
Math Is Book 6 (Ebos/Tuck) question 5(b) gives a surprising answer at the back of the book..

The question is:
Indicate the domain and range for this: y = sqr(x-9) (Square root of)

The answer for the domain is x>=9 which is not surprisingly, but the range is y>=0, yER ... which I could understand if you were not allowed to transform the equation into x as the subject..

But all example on the facing page DO TRANSFORM the equation at will with x and/or y as the subject..

Can you explain this...
??
Chris Fisher lui répond.

Square Root History 1997-08-29
Carlos Montecel S. pose la question :
I need find information over the "Square Root History", Could you help me?
Harley Weston lui répond.
Square Roots and Functions. 1997-04-23
Ed pose la question :
1. In most texts the solution to a question such as square root x = -6 is

x is undefined.

Yet when teaching to solve
xsquared = 36
x = +6 or -6

There appears to be a contradiction here. My question is when, where and why do we use the principle square root, not both + and -? This often occurs as the extraneous root in the solution of radical equations and in stating the domain and range of functions involving square roots.

2. Are there any simple rules for determining whether equations are functions without graphing them and doing a vertical line test?
Harley Weston lui répond.

Roots of a Polynomial 1996-12-06
Paula Miller pose la question :
Why is the solution called a "root"? Why not just the "x-intercepts"?
Chris Fisher and Harley Weston lui répond.
Approximating roots. 1996-11-04
Ben Dixon pose la question :
How do you calculate a square root? eg the square root of 2.

There is obviously some sort of successive approximation type algorithm for doing it to however many decimal places is required, but what is the algorithm?
Harley Weston lui répond.

Square roots 1996-03-16
Terry King and John pose la question :
We are just curious about how to manually calculate square roots.
Harley Weston lui répond.
The impossible problem 1996-03-15
Shaun Reynolds and Jacob Hiatt pose la question :
How do you solve (the 6th root of x)+4=3?
Penny Nom and Maxine Stinka lui répond.
Cardano's method 1996-03-11
Mike Gorski pose la question :
What is Cardano's method for finding the roots of a cubic equation?
Harley Weston lui répond.
Algorithms for roots 1996-02-22
Charles Hewitt pose la question :
I have seen an algorithm for finding the square root of numbers. Are there similar such algorithms for higher roots?
Harley Weston lui répond.
 
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