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

1 Answer
Jul 18, 2015

Answer:

#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.