Algebra Examples

$8 \sqrt[3]{5} - \sqrt[3]{40} - 2 \sqrt[3]{135}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $40$ as $2^{3} \cdot 5$ .

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Step 1.1.1

Factor $8$ out of $40$ .

$8 \sqrt[3]{5} - \sqrt[3]{8 (5)} - 2 \sqrt[3]{135}$

Step 1.1.2

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

$8 \sqrt[3]{5} - \sqrt[3]{2^{3} \cdot 5} - 2 \sqrt[3]{135}$

Step 1.2

Pull terms out from under the radical.

$8 \sqrt[3]{5} - (2 \sqrt[3]{5}) - 2 \sqrt[3]{135}$

Step 1.3

Multiply $2$ by $- 1$ .

$8 \sqrt[3]{5} - 2 \sqrt[3]{5} - 2 \sqrt[3]{135}$

Step 1.4

Rewrite $135$ as $3^{3} \cdot 5$ .

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Step 1.4.1

Factor $27$ out of $135$ .

$8 \sqrt[3]{5} - 2 \sqrt[3]{5} - 2 \sqrt[3]{27 (5)}$

Step 1.4.2

Rewrite $27$ as $3^{3}$ .

$8 \sqrt[3]{5} - 2 \sqrt[3]{5} - 2 \sqrt[3]{3^{3} \cdot 5}$

Step 1.5

Pull terms out from under the radical.

$8 \sqrt[3]{5} - 2 \sqrt[3]{5} - 2 (3 \sqrt[3]{5})$

Step 1.6

Multiply $3$ by $- 2$ .

$8 \sqrt[3]{5} - 2 \sqrt[3]{5} - 6 \sqrt[3]{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 \sqrt[3]{5}$ from $8 \sqrt[3]{5}$ .

$6 \sqrt[3]{5} - 6 \sqrt[3]{5}$

Step 2.2

Subtract $6 \sqrt[3]{5}$ from $6 \sqrt[3]{5}$ .

$0$