Algebra Examples

$\sqrt{64 a^{4} b^{5}} - \sqrt[3]{64 a^{5} b^{4}}$

Step 1

Rewrite $64 a^{4} b^{5}$ as ${(8 a^{2} b^{2})}^{2} b$ .

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Step 1.1

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} a^{4} b^{5}} - \sqrt[3]{64 a^{5} b^{4}}$

Step 1.2

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$\sqrt{8^{2} {(a^{2})}^{2} b^{5}} - \sqrt[3]{64 a^{5} b^{4}}$

Step 1.3

Factor out $b^{4}$ .

$\sqrt{8^{2} {(a^{2})}^{2} (b^{4} b)} - \sqrt[3]{64 a^{5} b^{4}}$

Step 1.4

Rewrite $b^{4}$ as ${(b^{2})}^{2}$ .

$\sqrt{8^{2} {(a^{2})}^{2} ({(b^{2})}^{2} b)} - \sqrt[3]{64 a^{5} b^{4}}$

Step 1.5

Rewrite $8^{2} {(a^{2})}^{2} {(b^{2})}^{2}$ as ${(8 a^{2} b^{2})}^{2}$ .

$\sqrt{{(8 a^{2} b^{2})}^{2} b} - \sqrt[3]{64 a^{5} b^{4}}$

Step 2

Pull terms out from under the radical.

$8 a^{2} b^{2} \sqrt{b} - \sqrt[3]{64 a^{5} b^{4}}$

Step 3

Rewrite $64 a^{5} b^{4}$ as ${(4 a b)}^{3} (a^{2} b)$ .

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Step 3.1

Rewrite $64$ as $4^{3}$ .

$8 a^{2} b^{2} \sqrt{b} - \sqrt[3]{4^{3} a^{5} b^{4}}$

Step 3.2

Factor out $a^{3}$ .

$8 a^{2} b^{2} \sqrt{b} - \sqrt[3]{4^{3} (a^{3} a^{2}) b^{4}}$

Step 3.3

Factor out $b^{3}$ .

$8 a^{2} b^{2} \sqrt{b} - \sqrt[3]{4^{3} (a^{3} a^{2}) (b^{3} b)}$

Step 3.4

Move $a^{2}$ .

$8 a^{2} b^{2} \sqrt{b} - \sqrt[3]{4^{3} a^{3} b^{3} a^{2} b}$

Step 3.5

Rewrite $4^{3} (a^{3}) b^{3}$ as ${(4 a b)}^{3}$ .

$8 a^{2} b^{2} \sqrt{b} - \sqrt[3]{{(4 a b)}^{3} a^{2} b}$

Step 3.6

Add parentheses.

$8 a^{2} b^{2} \sqrt{b} - \sqrt[3]{{(4 a b)}^{3} (a^{2} b)}$

Step 4

Pull terms out from under the radical.

$8 a^{2} b^{2} \sqrt{b} - (4 a b \sqrt[3]{a^{2} b})$

Step 5

Multiply $4$ by $- 1$ .

$8 a^{2} b^{2} \sqrt{b} - 4 a b \sqrt[3]{a^{2} b}$