Simplify the Radical Expression 6 fourth root of 405

$6 \sqrt[4]{405}$

Step 1

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

Factor $81$ out of $405$ .

$6 \sqrt[4]{81 (5)}$

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

$6 \sqrt[4]{3^{4} \cdot 5}$

Step 2

Pull terms out from under the radical.

$6 (| 3 | \sqrt[4]{5})$

Step 3

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

$6 (3 \sqrt[4]{5})$

Step 4

Multiply $3$ by $6$ .

$18 \sqrt[4]{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$18 \sqrt[4]{5}$

Decimal Form:

$26.91627806 \dots$