Algebra Examples

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

Step 1

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

$\sqrt[3]{9 - \sqrt{4 - \sqrt{3^{2}}}}$

Step 2

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

$\sqrt[3]{9 - \sqrt{4 - 1 \cdot 3}}$

Step 3

Multiply $- 1$ by $3$ .

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

Step 4

Subtract $3$ from $4$ .

$\sqrt[3]{9 - \sqrt{1}}$

Step 5

Any root of $1$ is $1$ .

$\sqrt[3]{9 - 1 \cdot 1}$

Step 6

Multiply $- 1$ by $1$ .

$\sqrt[3]{9 - 1}$

Step 7

Subtract $1$ from $9$ .

$\sqrt[3]{8}$

Step 8

Rewrite $8$ as $2^{3}$ .

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

Step 9

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

$2$