Simplify fourth root of 324

$\sqrt[4]{324}$

Step 1

Rewrite $324$ as $3^{4} \cdot 4$ .

Factor $81$ out of $324$ .

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

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

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

Step 2

Pull terms out from under the radical.

$3 \sqrt[4]{4}$

Step 3

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

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

Step 4

Rewrite $\sqrt[4]{2^{2}}$ as $\sqrt{\sqrt{2^{2}}}$ .

$3 \sqrt{\sqrt{2^{2}}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$3 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$