Simplify the Radical Expression 3 fourth root of 8*7 fourth root of 32

$3 \sqrt[4]{8} \cdot 7 \sqrt[4]{32}$

Step 1

Multiply $7$ by $3$ .

$21 \sqrt[4]{8} \sqrt[4]{32}$

Step 2

Rewrite $32$ as $2^{4} \cdot 2$ .

Factor $16$ out of $32$ .

$21 \sqrt[4]{8} \sqrt[4]{16 (2)}$

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

$21 \sqrt[4]{8} \sqrt[4]{2^{4} \cdot 2}$

Step 3

Pull terms out from under the radical.

$21 \sqrt[4]{8} (| 2 | \sqrt[4]{2})$

Step 4

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

$21 \sqrt[4]{8} (2 \sqrt[4]{2})$

Step 5

Multiply $21 \sqrt[4]{8} (2 \sqrt[4]{2})$ .

Multiply $2$ by $21$ .

$42 \sqrt[4]{8} \sqrt[4]{2}$

Combine using the product rule for radicals.

$42 \sqrt[4]{2 \cdot 8}$

Multiply $2$ by $8$ .

$42 \sqrt[4]{16}$

Step 6

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

$42 \sqrt[4]{2^{4}}$

Step 7

Pull terms out from under the radical.

$42 | 2 |$

Step 8

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

$42 \cdot 2$

Step 9

Multiply $42$ by $2$ .

$84$