Simplify the Radical Expression 7 cube root of 3+2 cube root of 192

$7 \sqrt[3]{3} + 2 \sqrt[3]{192}$

Step 1

Simplify each term.

Rewrite $192$ as $4^{3} \cdot 3$ .

Factor $64$ out of $192$ .

$7 \sqrt[3]{3} + 2 \sqrt[3]{64 (3)}$

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

$7 \sqrt[3]{3} + 2 \sqrt[3]{4^{3} \cdot 3}$

Pull terms out from under the radical.

$7 \sqrt[3]{3} + 2 (4 \sqrt[3]{3})$

Multiply $4$ by $2$ .

$7 \sqrt[3]{3} + 8 \sqrt[3]{3}$

Step 2

Add $7 \sqrt[3]{3}$ and $8 \sqrt[3]{3}$ .

$15 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt[3]{3}$

Decimal Form:

$21.63374355 \dots$