Simplify cube root of 16y^3

$\sqrt[3]{16 y^{3}}$

Step 1

Rewrite $16 y^{3}$ as ${(2 y)}^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2) y^{3}}$

Rewrite $8$ as $2^{3}$ .

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

Move $2$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

$2 y \sqrt[3]{2}$

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