Simplify the Radical Expression 8 square root of 16-2 cube root of 8+ fourth root of 16

$8 \sqrt{16} - 2 \sqrt[3]{8} + \sqrt[4]{16}$

Step 1

Simplify each term.

Rewrite $16$ as $4^{2}$ .

$8 \sqrt{4^{2}} - 2 \sqrt[3]{8} + \sqrt[4]{16}$

Pull terms out from under the radical.

$8 | 4 | - 2 \sqrt[3]{8} + \sqrt[4]{16}$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$8 \cdot 4 - 2 \sqrt[3]{8} + \sqrt[4]{16}$

Multiply $8$ by $4$ .

$32 - 2 \sqrt[3]{8} + \sqrt[4]{16}$

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

$32 - 2 \sqrt[3]{2^{3}} + \sqrt[4]{16}$

Pull terms out from under the radical.

$32 - 2 \cdot 2 + \sqrt[4]{16}$

Multiply $- 2$ by $2$ .

$32 - 4 + \sqrt[4]{16}$

Rewrite $16$ as $2^{4}$ .

$32 - 4 + \sqrt[4]{2^{4}}$

Pull terms out from under the radical.

$32 - 4 + | 2 |$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$32 - 4 + 2$

Step 2

Subtract $4$ from $32$ .

$28 + 2$

Step 3

Add $28$ and $2$ .

$30$