Simplify cube root of 81x^2

$\sqrt[3]{81 x^{2}}$

Rewrite $81 x^{2}$ as $3^{3} \cdot (3 x^{2})$ .

Factor $27$ out of $81$ .

$\sqrt[3]{27 (3) x^{2}}$

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{3^{3} \cdot 3 x^{2}}$

Add parentheses.

$\sqrt[3]{3^{3} \cdot (3 x^{2})}$

$\sqrt[3]{3^{3} \cdot (3 x^{2})}$

Pull terms out from under the radical.

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

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