Simplify the Radical Expression 8 fourth root of 32- fourth root of 162

$8 \sqrt[4]{32} - \sqrt[4]{162}$

Simplify each term.

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

Factor $16$ out of $32$ .

$8 \sqrt[4]{16 (2)} - \sqrt[4]{162}$

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

$8 \sqrt[4]{2^{4} \cdot 2} - \sqrt[4]{162}$

Pull terms out from under the radical.

$8 (| 2 | \sqrt[4]{2}) - \sqrt[4]{162}$

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

$8 (2 \sqrt[4]{2}) - \sqrt[4]{162}$

Multiply $2$ by $8$ .

$16 \sqrt[4]{2} - \sqrt[4]{162}$

Rewrite $162$ as $3^{4} \cdot 2$ .

Factor $81$ out of $162$ .

$16 \sqrt[4]{2} - \sqrt[4]{81 (2)}$

Rewrite $81$ as $3^{4}$ .

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

Pull terms out from under the radical.

$16 \sqrt[4]{2} - (| 3 | \sqrt[4]{2})$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$16 \sqrt[4]{2} - (3 \sqrt[4]{2})$

Multiply $3$ by $- 1$ .

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

Subtract $3 \sqrt[4]{2}$ from $16 \sqrt[4]{2}$ .

$13 \sqrt[4]{2}$

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt[4]{2}$

Decimal Form:

$15.45969249 \dots$