Simplify cube root of 24m^3

$\sqrt[3]{24 m^{3}}$

Step 1

Rewrite $24 m^{3}$ as ${(2 m)}^{3} \cdot 3$ .

Factor $8$ out of $24$ .

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

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

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

Move $3$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

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

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