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Simplify -6 cube root of 250+ cube root of 16

$- 6 \sqrt[3]{250} + \sqrt[3]{16}$

Step 1

Simplify each term.

Rewrite

$250$ as

$5^{3} \cdot 2$ .

Factor

$125$ out of

$250$ .

$- 6 \sqrt[3]{125 (2)} + \sqrt[3]{16}$

Rewrite

$125$ as

$5^{3}$ .

$- 6 \sqrt[3]{5^{3} \cdot 2} + \sqrt[3]{16}$

$- 6 \sqrt[3]{5^{3} \cdot 2} + \sqrt[3]{16}$

Pull terms out from under the radical.

$- 6 (5 \sqrt[3]{2}) + \sqrt[3]{16}$

Multiply

$5$ by

$- 6$ .

$- 30 \sqrt[3]{2} + \sqrt[3]{16}$

Rewrite

$16$ as

$2^{3} \cdot 2$ .

Factor

$8$ out of

$16$ .

$- 30 \sqrt[3]{2} + \sqrt[3]{8 (2)}$

Rewrite

$8$ as

$2^{3}$ .

$- 30 \sqrt[3]{2} + \sqrt[3]{2^{3} \cdot 2}$

$- 30 \sqrt[3]{2} + \sqrt[3]{2^{3} \cdot 2}$

Pull terms out from under the radical.

$- 30 \sqrt[3]{2} + 2 \sqrt[3]{2}$

$- 30 \sqrt[3]{2} + 2 \sqrt[3]{2}$

Step 2

Add

$- 30 \sqrt[3]{2}$ and

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

$- 28 \sqrt[3]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 28 \sqrt[3]{2}$

Decimal Form:

$- 35.27778939 \dots$

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