Simplify fourth root of 100

$\sqrt[4]{100}$

Step 1

Rewrite $100$ as $10^{2}$ .

$\sqrt[4]{10^{2}}$

Step 2

Rewrite $\sqrt[4]{10^{2}}$ as $\sqrt{\sqrt{10^{2}}}$ .

$\sqrt{\sqrt{10^{2}}}$

Step 3

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

$\sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$