Question

I'm having trouble understanding when I am supposed to add absolute values when simplifying radicals.

(It's cube root not square root)

XER and YER because it's a cube root and you can take cube root of negatives and positives.

√-108x^7y^9
= √-27•4•x^6•x•x^9
= -3x^2y √4x
= -3x^2|y|√4x

So for this one would it be simplified to: 3x^2y √4x or -3x^2|y|√4x. And why.

Answer 1

(-108 x^7 y^9)^(1/3)

(-27 * 4 * x^6 * x^1 * y^9)^(1/3)

-3 * x^2 * y^3 *(4 x)^(1/3)

Answer 2

Would I need to add || absolute value around any variables?

Answer 3

well if x is negative, then x^1 and x^7 are negative and x^6 is + so you do not want ||
if y^9 is negative then y wants to be - and y^3 will be negative so again not || needed