Algebra Examples

$\sqrt[12]{729}$

Step 1

Rewrite $729$ as $9^{3}$ .

$\sqrt[12]{9^{3}}$

Step 2

Rewrite $\sqrt[12]{9^{3}}$ as $\sqrt[4]{\sqrt[3]{9^{3}}}$ .

$\sqrt[4]{\sqrt[3]{9^{3}}}$

Step 3

Pull terms out from under the radical.

$\sqrt[4]{9}$

Step 4

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

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

Step 5

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

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

Step 6

Pull terms out from under the radical.

$\sqrt{| 3 |}$

Step 7

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

$\sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$