Precalculus Examples

$5 a \sqrt[3]{24 a^{2}} + 3 \sqrt[3]{4 b^{4}} - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $8$ out of $24$ .

$5 a \sqrt[3]{8 (3) a^{2}} + 3 \sqrt[3]{4 b^{4}} - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.1.2

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

$5 a \sqrt[3]{2^{3} \cdot 3 a^{2}} + 3 \sqrt[3]{4 b^{4}} - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.1.3

Add parentheses.

$5 a \sqrt[3]{2^{3} \cdot (3 a^{2})} + 3 \sqrt[3]{4 b^{4}} - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.2

Pull terms out from under the radical.

$5 a (2 \sqrt[3]{3 a^{2}}) + 3 \sqrt[3]{4 b^{4}} - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.3

Multiply $2$ by $5$ .

$10 a \sqrt[3]{3 a^{2}} + 3 \sqrt[3]{4 b^{4}} - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.4

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

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Step 1.4.1

Factor out $b^{3}$ .

$10 a \sqrt[3]{3 a^{2}} + 3 \sqrt[3]{4 (b^{3} b)} - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.4.2

Reorder $4$ and $b^{3}$ .

$10 a \sqrt[3]{3 a^{2}} + 3 \sqrt[3]{b^{3} \cdot 4 b} - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.4.3

Add parentheses.

$10 a \sqrt[3]{3 a^{2}} + 3 \sqrt[3]{b^{3} \cdot (4 b)} - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.5

Pull terms out from under the radical.

$10 a \sqrt[3]{3 a^{2}} + 3 (b \sqrt[3]{4 b}) - \sqrt[3]{192 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.6

Rewrite $192 a^{5}$ as ${(4 a)}^{3} \cdot (3 a^{2})$ .

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Step 1.6.1

Factor $64$ out of $192$ .

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - \sqrt[3]{64 (3) a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.6.2

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

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - \sqrt[3]{4^{3} \cdot 3 a^{5}} - 6 b \sqrt[3]{32 b}$

Step 1.6.3

Factor out $a^{3}$ .

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - \sqrt[3]{4^{3} \cdot 3 (a^{3} a^{2})} - 6 b \sqrt[3]{32 b}$

Step 1.6.4

Move $3$ .

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - \sqrt[3]{4^{3} a^{3} \cdot 3 a^{2}} - 6 b \sqrt[3]{32 b}$

Step 1.6.5

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

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - \sqrt[3]{{(4 a)}^{3} \cdot 3 a^{2}} - 6 b \sqrt[3]{32 b}$

Step 1.6.6

Add parentheses.

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - \sqrt[3]{{(4 a)}^{3} \cdot (3 a^{2})} - 6 b \sqrt[3]{32 b}$

Step 1.7

Pull terms out from under the radical.

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - (4 a \sqrt[3]{3 a^{2}}) - 6 b \sqrt[3]{32 b}$

Step 1.8

Multiply $4$ by $- 1$ .

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - 4 (a \sqrt[3]{3 a^{2}}) - 6 b \sqrt[3]{32 b}$

Step 1.9

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

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Step 1.9.1

Factor $8$ out of $32$ .

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - 4 a \sqrt[3]{3 a^{2}} - 6 b \sqrt[3]{8 (4) b}$

Step 1.9.2

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

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - 4 a \sqrt[3]{3 a^{2}} - 6 b \sqrt[3]{2^{3} \cdot 4 b}$

Step 1.9.3

Add parentheses.

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - 4 a \sqrt[3]{3 a^{2}} - 6 b \sqrt[3]{2^{3} \cdot (4 b)}$

Step 1.10

Pull terms out from under the radical.

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - 4 a \sqrt[3]{3 a^{2}} - 6 b (2 \sqrt[3]{4 b})$

Step 1.11

Multiply $2$ by $- 6$ .

$10 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - 4 a \sqrt[3]{3 a^{2}} - 12 b \sqrt[3]{4 b}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $4 a \sqrt[3]{3 a^{2}}$ from $10 a \sqrt[3]{3 a^{2}}$ .

$6 a \sqrt[3]{3 a^{2}} + 3 b \sqrt[3]{4 b} - 12 b \sqrt[3]{4 b}$

Step 2.2

Subtract $12 b \sqrt[3]{4 b}$ from $3 b \sqrt[3]{4 b}$ .

$6 a \sqrt[3]{3 a^{2}} - 9 b \sqrt[3]{4 b}$