Simplify the Radical Expression fourth root of 10* fourth root of 10

$\sqrt[4]{10} \cdot \sqrt[4]{10}$

Combine using the product rule for radicals.

$\sqrt[4]{10 \cdot 10}$

Multiply $10$ by $10$ .

$\sqrt[4]{100}$

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

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

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

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

Pull terms out from under the radical.

$\sqrt{| 10 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$\sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$