Simplify square root of cube root of 25

$\sqrt{\sqrt[3]{25}}$

Step 1

Rewrite $\sqrt{\sqrt[3]{25}}$ as $\sqrt[6]{25}$ .

$\sqrt[6]{25}$

Step 2

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

$\sqrt[6]{5^{2}}$

Step 3

Rewrite $\sqrt[6]{5^{2}}$ as $\sqrt[3]{\sqrt{5^{2}}}$ .

$\sqrt[3]{\sqrt{5^{2}}}$

Step 4

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

$\sqrt[3]{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{5}$

Decimal Form:

$1.70997594 \dots$