Simplify the Radical Expression square root of fourth root of 25

$\sqrt{\sqrt[4]{25}}$

Step 1

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

$\sqrt{\sqrt[4]{5^{2}}}$

Step 2

Rewrite $\sqrt[4]{5^{2}}$ as $\sqrt{\sqrt{5^{2}}}$ .

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

Step 3

Pull terms out from under the radical.

$\sqrt{\sqrt{| 5 |}}$

Step 4

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

$\sqrt{\sqrt{5}}$

Step 5

Rewrite $\sqrt{\sqrt{5}}$ as $\sqrt[4]{5}$ .

$\sqrt[4]{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt[4]{5}$

Decimal Form:

$1.49534878 \dots$