Question

What is the square root of (x^6)/27?

Answer 1

`sqrt((x^6)/27) = sqrt(3)/9 abs(x^3)`

Explanation:

If `a, b >= 0` then `sqrt(ab) = sqrt(a)sqrt(b)` and `sqrt(a/b) = sqrt(a)/sqrt(b)`

`sqrt((x^6)/27) = sqrt((3x^6)/81) = (sqrt(x^6)sqrt(3))/sqrt(81) = (abs(x^3)sqrt(3))/9 = sqrt(3)/9 abs(x^3)`

Note `abs(x^3)`, not `x^3`.

If `x < 0` then `x^3 < 0`, but `sqrt(x^6) > 0` since `sqrt` denotes the positive square root.