Question 186067
find x if (Sqrt x sqrt x)^3=9 
Assume you mean
{{{(sqrt(x*sqrt(x)))^3}}} = 9
:
Find the cube root of both sides
{{{sqrt(x*sqrt(x))}}} = {{{9^(1/3)}}}
Write it using exponents on the inside radical
{{{sqrt(x*x^(1/2))}}} = {{{9^(1/3)}}}
:
{{{sqrt(x^(3/2))}}} = {{{9^(1/3)}}}
:
{{{(x^(3/2))^(1/2)}}} = {{{9^(1/3)}}}
:
{{{x^(3/4)}}} = {{{9^(1/3)}}}
Cube both sides
{{{(x^(3/4))^3}}} = 9
:
{{{x^(9/4)}}} = 9
:
x = {{{9^(4/9)}}}
x ~ 2.655
:
:
Check solution on a calc: enter {{{(sqrt(2.655*sqrt(2.655)))^3}}} = 8.997 ~ 9