How would you simplify #sqrt (9x^3)#?

1 Answer
Feb 1, 2016

Answer:

#3xsqrt(x)#

Explanation:

We start out with #sqrt(9x^3)#. To solve this we simplify the values into their smallest factors. For #9#, that's pretty easy; the smallest it goes is #3*3# or #3^2#. #x^3# can be simplified to #x*x*x# or #x^2*x#.

If we rewrite the expression, it becomes #sqrt(3^2*x^2*x)#. Square root of a square cancels out, like this #cancel(sqrt(3^cancel(2)#.

#sqrt(3^2)# is just #3#. Likewise #sqrt(x^2)# simplifys to #x#. Now the expression is #3xsqrtx#.