# How do you solve #root3(x^2)= 9#?

##### 2 Answers

Mar 30, 2017

#### Answer:

#### Explanation:

Given:

#root(3)(x^2)=9#

Note that

#root(3)(x^2) = 3^2#

Note that both

Cubing both sides of the equation, we get:

#x^2 = (3^2)^3 = 3^(2*3) = 3^(3*2) = (3^3)^2 = 27^2#

Subtract

#x^2-27^2 = 0#

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

Using this with

#0 = x^2-27^2 = (x-27)(x+27)#

So:

#x = +-27#