Algebra Examples

$\sqrt[3]{32 a^{5}}$

Step 1

Rewrite $32 a^{5}$ as ${(2 a)}^{3} \cdot (4 a^{2})$ .

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Step 1.1

Factor $8$ out of $32$ .

$\sqrt[3]{8 (4) a^{5}}$

Step 1.2

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

$\sqrt[3]{2^{3} \cdot 4 a^{5}}$

Step 1.3

Factor out $a^{3}$ .

$\sqrt[3]{2^{3} \cdot 4 (a^{3} a^{2})}$

Step 1.4

Move $4$ .

$\sqrt[3]{2^{3} a^{3} \cdot 4 a^{2}}$

Step 1.5

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

$\sqrt[3]{{(2 a)}^{3} \cdot 4 a^{2}}$

Step 1.6

Add parentheses.

$\sqrt[3]{{(2 a)}^{3} \cdot (4 a^{2})}$

Step 2

Pull terms out from under the radical.

$2 a \sqrt[3]{4 a^{2}}$