Simplify 3/4 cube root of 128+2/5 cube root of 250

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

Simplify each term.

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

Factor $64$ out of $128$ .

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

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

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

Pull terms out from under the radical.

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

Cancel the common factor of $4$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $125$ out of $250$ .

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

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

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

Pull terms out from under the radical.

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

Cancel the common factor of $5$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

$5 \sqrt[3]{2}$

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt[3]{2}$

Decimal Form:

$6.29960524 \dots$