Simplify the Radical Expression fourth root of 144

$\sqrt[4]{144}$

Step 1

Rewrite $144$ as $2^{4} \cdot 9$ .

Factor $16$ out of $144$ .

$\sqrt[4]{16 (9)}$

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

$\sqrt[4]{2^{4} \cdot 9}$

Step 2

Pull terms out from under the radical.

$| 2 | \sqrt[4]{9}$

Step 3

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

$2 \sqrt[4]{9}$

Step 4

Rewrite $9$ as $3^{2}$ .

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

Step 5

Rewrite $\sqrt[4]{3^{2}}$ as $\sqrt{\sqrt{3^{2}}}$ .

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

Step 6

Pull terms out from under the radical.

$2 \sqrt{| 3 |}$

Step 7

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

$2 \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3}$

Decimal Form:

$3.46410161 \dots$