SOLUTION: Take a factor out of the square root: 48x^2 , where x≤0 Answer?

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Question 1134201: Take a factor out of the square root:
48x^2 , where x≤0
Answer?
Found 3 solutions by Theo, ikleyn, josgarithmetic:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i'm not exactly sure waht you're looking for her.

if you take the square root of (48x^2), then that could be shown as:

sqrt(48 * x^2) = sqrt(48) * sqrt(x^2) = sqrt(3 * 16) * sqrt(x^2) = sqrt(3) * sqrt(16) * sqrt(x^2) = sqrt(3) * 4 * |x|.

your final simplified answer would be sqrt(3) * 4 * |x|.

x can be any real value.

for example:

when x = -5, sqrt (48 * x^2) = sqrt(48 * 25) = sqrt(1200) = 34.64101615.

sqrt(3) * 4 * |x| = sqrt(3) * 4 * |-5| = sqrt(3) * 4 * 5 = 34.64101615.

something to keep in mind.

if x^2 = 25, then x = plus or minus 25, but sqrt(25) is always equal to 5 and not -5.

here's a reference.

https://www.physicsforums.com/threads/a-proof-for-sqrt-x-2-x.316896/

here's another reference.

https://socratic.org/questions/what-is-the-square-root-of-x-squared

here's another reference.

https://www.mathsisfun.com/algebra/square-root.html

Answer by ikleyn(52866) About Me  (Show Source):
You can put this solution on YOUR website!
.
The meaning of this post is totally unclear.

I mean - "mathematical meaning" of the post and of the problem.


---------------- 

Also, this form to ask for a solution and for help //  "Answer ? " // which you use in the post,

is incorrect from the point of view of the rules accepted between educated people.



My advise to you is to avoid such form communicating with people (and concretely with the tutors of this forum), 

with whom you are not familiar personally and briefly.


Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
---------------------------------
Take a factor out of the square root:
48x^2 , where x≤0
Answer?
--------------------------------

?

x^2 is positive if x is negative; or x^2 is 0 if x is 0.
How do you mean, "take out a factor"?
sqrt%2848x%5E2%29
sqrt%2848%29%2Asqrt%28x%5E2%29
sqrt%282%2A2%2A2%2A2%2A3%29%2Aabs%28x%29
4%2Aabs%28x%29%2Asqrt%286%29
You decide what factor you wanted taken out.