Simplify cube root of 6(5+ cube root of 12)

$\sqrt[3]{6} (5 + \sqrt[3]{12})$

Step 1

Simplify terms.

Apply the distributive property.

$\sqrt[3]{6} \cdot 5 + \sqrt[3]{6} \sqrt[3]{12}$

Move $5$ to the left of $\sqrt[3]{6}$ .

$5 \cdot \sqrt[3]{6} + \sqrt[3]{6} \sqrt[3]{12}$

Combine using the product rule for radicals.

$5 \cdot \sqrt[3]{6} + \sqrt[3]{6 \cdot 12}$

$5 \cdot \sqrt[3]{6} + \sqrt[3]{6 \cdot 12}$

Step 2

Simplify each term.

Multiply $6$ by $12$ .

$5 \sqrt[3]{6} + \sqrt[3]{72}$

Rewrite $72$ as $2^{3} \cdot 9$ .

Factor $8$ out of $72$ .

$5 \sqrt[3]{6} + \sqrt[3]{8 (9)}$

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

$5 \sqrt[3]{6} + \sqrt[3]{2^{3} \cdot 9}$

$5 \sqrt[3]{6} + \sqrt[3]{2^{3} \cdot 9}$

Pull terms out from under the radical.

$5 \sqrt[3]{6} + 2 \sqrt[3]{9}$

$5 \sqrt[3]{6} + 2 \sqrt[3]{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt[3]{6} + 2 \sqrt[3]{9}$

Decimal Form:

$13.24577061 \dots$

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