Algebra Examples

$\sqrt[12]{64}$

Step 1

Rewrite $64$ as $4^{3}$ .

$\sqrt[12]{4^{3}}$

Step 2

Rewrite $\sqrt[12]{4^{3}}$ as $\sqrt[4]{\sqrt[3]{4^{3}}}$ .

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

Step 3

Pull terms out from under the radical.

$\sqrt[4]{4}$

Step 4

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

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

Step 5

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

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

Step 6

Pull terms out from under the radical.

$\sqrt{| 2 |}$

Step 7

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

$\sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$