Simplify the Radical Expression square root of square root of square root of 625

$\sqrt{\sqrt{\sqrt{625}}}$

Step 1

Rewrite $625$ as $25^{2}$ .

$\sqrt{\sqrt{\sqrt{25^{2}}}}$

Step 2

Pull terms out from under the radical.

$\sqrt{\sqrt{| 25 |}}$

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $25$ is $25$ .

$\sqrt{\sqrt{25}}$

Step 4

Rewrite $25$ as $5^{2}$ .

$\sqrt{\sqrt{5^{2}}}$

Step 5

Pull terms out from under the radical.

$\sqrt{| 5 |}$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$\sqrt{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$