Simplify square root of 9x^3

$\sqrt{9 x^{3}}$

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

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

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

Factor out $x^{2}$ .

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

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

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

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

Pull terms out from under the radical.

$3 x \sqrt{x}$

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