Simplify the Radical Expression fourth root of 81+ fourth root of 32- fourth root of 2

$\sqrt[4]{81} + \sqrt[4]{32} - \sqrt[4]{2}$

Simplify each term.

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

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

Pull terms out from under the radical.

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

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

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

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

Factor $16$ out of $32$ .

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

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

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

Pull terms out from under the radical.

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

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

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

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

$3 + \sqrt[4]{2}$

The result can be shown in multiple forms.

Exact Form:

$3 + \sqrt[4]{2}$

Decimal Form:

$4.18920711 \dots$