Simplify the Radical Expression ( fourth root of 810)/( fourth root of 2)

$\frac{\sqrt[4]{810}}{\sqrt[4]{2}}$

Step 1

Combine $\sqrt[4]{810}$ and $\sqrt[4]{2}$ into a single radical.

$\sqrt[4]{\frac{810}{2}}$

Step 2

Divide $810$ by $2$ .

$\sqrt[4]{405}$

Step 3

Rewrite $405$ as $3^{4} \cdot 5$ .

Factor $81$ out of $405$ .

$\sqrt[4]{81 (5)}$

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

$\sqrt[4]{3^{4} \cdot 5}$

Step 4

Pull terms out from under the radical.

$| 3 | \sqrt[4]{5}$

Step 5

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

$3 \sqrt[4]{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[4]{5}$

Decimal Form:

$4.48604634 \dots$