Trigonometry Examples

$\sqrt[12]{16} = \sqrt[3]{\sqrt[4]{16}}$

Step 1

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

$\sqrt[12]{2^{4}} = \sqrt[3]{\sqrt[4]{16}}$

Step 2

Rewrite $\sqrt[12]{2^{4}}$ as $\sqrt[3]{\sqrt[4]{2^{4}}}$ .

$\sqrt[3]{\sqrt[4]{2^{4}}} = \sqrt[3]{\sqrt[4]{16}}$

Step 3

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

$\sqrt[3]{2} = \sqrt[3]{\sqrt[4]{16}}$

Step 4

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

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

Step 5

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

$\sqrt[3]{2} = \sqrt[3]{2}$

Step 6

Since the two sides have been shown to be equivalent, the equation is an identity.

$\sqrt[12]{16} = \sqrt[3]{\sqrt[4]{16}}$ is an identity.