Simplify the Radical Expression square root of 9x^7

$\sqrt{9 x^{7}}$

Rewrite $9 x^{7}$ as ${(3 x^{3})}^{2} x$ .

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} x^{7}}$

Factor out $x^{6}$ .

$\sqrt{3^{2} (x^{6} x)}$

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

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

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

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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