Algebra Examples

$\frac{3}{4} \sqrt[3]{128} + \frac{2}{5} \sqrt[3]{250}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $128$ as $4^{3} \cdot 2$ .

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Step 1.1.1

Factor $64$ out of $128$ .

$\frac{3}{4} \cdot \sqrt[3]{64 (2)} + \frac{2}{5} \cdot \sqrt[3]{250}$

Step 1.1.2

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

$\frac{3}{4} \cdot \sqrt[3]{4^{3} \cdot 2} + \frac{2}{5} \cdot \sqrt[3]{250}$

Step 1.2

Pull terms out from under the radical.

$\frac{3}{4} \cdot (4 \sqrt[3]{2}) + \frac{2}{5} \cdot \sqrt[3]{250}$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Factor $4$ out of $4 \sqrt[3]{2}$ .

$\frac{3}{4} \cdot (4 (\sqrt[3]{2})) + \frac{2}{5} \cdot \sqrt[3]{250}$

Step 1.3.2

Cancel the common factor.

$\frac{3}{4} \cdot (4 \sqrt[3]{2}) + \frac{2}{5} \cdot \sqrt[3]{250}$

Step 1.3.3

Rewrite the expression.

$3 \cdot \sqrt[3]{2} + \frac{2}{5} \cdot \sqrt[3]{250}$

Step 1.4

Rewrite $250$ as $5^{3} \cdot 2$ .

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Step 1.4.1

Factor $125$ out of $250$ .

$3 \sqrt[3]{2} + \frac{2}{5} \cdot \sqrt[3]{125 (2)}$

Step 1.4.2

Rewrite $125$ as $5^{3}$ .

$3 \sqrt[3]{2} + \frac{2}{5} \cdot \sqrt[3]{5^{3} \cdot 2}$

Step 1.5

Pull terms out from under the radical.

$3 \sqrt[3]{2} + \frac{2}{5} \cdot (5 \sqrt[3]{2})$

Step 1.6

Cancel the common factor of $5$ .

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Step 1.6.1

Factor $5$ out of $5 \sqrt[3]{2}$ .

$3 \sqrt[3]{2} + \frac{2}{5} \cdot (5 (\sqrt[3]{2}))$

Step 1.6.2

Cancel the common factor.

$3 \sqrt[3]{2} + \frac{2}{5} \cdot (5 \sqrt[3]{2})$

Step 1.6.3

Rewrite the expression.

$3 \sqrt[3]{2} + 2 \cdot \sqrt[3]{2}$

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

Step 2

Add $3 \sqrt[3]{2}$ and $2 \sqrt[3]{2}$ .

$5 \sqrt[3]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt[3]{2}$

Decimal Form:

$6.29960524 \dots$