Question 479289: Hi. Here is the problem I'm stuck on. The math problem says to simplify the expression.
I know the square root of 864 is 12 sqrt 6, but I don't know what to do with the x^2.
Found 4 solutions by MathLover1, Theo, ikleyn, greenestamps:
Answer by MathLover1(20850)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! you want to simplify sqrt(864*x^2)
the x^2 under the square root can be taken out from under the square root sign by taking the square root of it.
since the square root of x^2 is equal to x, your equation then becomes:
x*sqrt(864)
since 864 is equal to 6*144 and 144 is a perfect square, you can bring it out from under the square root sign by taking the square root of it, as you did.
you are left with:
x * 12 * sqrt(6)
your answer is:
12x*sqrt(6)
Answer by ikleyn(52950)  (Show Source):
You can put this solution on YOUR website! .
Hi. Here is the problem I'm stuck on. The math problem says to simplify the expression.
I know the square root of 864 is 12 sqrt 6, but I don't know what to do with the x^2.
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The answers in the posts by tutors @Theo and @MathLover1, giving 12x*sqrt(6), both are incorrect.
The correct answer is 12*|x|*sqrt(6).
The @Theo's answer and the @MathLover1's answer are valid only for non-negative 'x'.
For negative values of 'x' they are wrong.
But in the original expression, 'x' can be negative, too.
In this case, the @Theo's answer and the @MathLover1 answer both are INCORRECT,
while my answer works for both cases non-negative and negative values of 'x',
so, it is universally correct.
It is very important to know what is a correct expression for  .
It is not 'x', as 99% of people and 90% of teachers and tutors think.
The correct expression is |x|.
99% of students of middle school and of high school don't know it.
For you, reading this my post is the rare and the happy opportunity to learn the truth.
Answer by greenestamps(13219)  (Show Source):
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