Simplify square root of x^7

$\sqrt{x^{7}}$

Rewrite $x^{7}$ as ${(x^{3})}^{2} x$ .

Factor out $x^{6}$ .

$\sqrt{x^{6} x}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt{{(x^{3})}^{2} x}$

Pull terms out from under the radical.

$x^{3} \sqrt{x}$