Simplify the Radical Expression square root of square root of 81

$\sqrt{\sqrt{81}}$

Step 1

Rewrite $81$ as $9^{2}$ .

$\sqrt{\sqrt{9^{2}}}$

Step 2

Pull terms out from under the radical.

$\sqrt{| 9 |}$

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $9$ is $9$ .

$\sqrt{9}$

Step 4

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

$\sqrt{3^{2}}$

Step 5

Pull terms out from under the radical.

$| 3 |$

Step 6

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

$3$