Simplify fourth root of 10* fourth root of 10

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

Step 1

Combine using the product rule for radicals.

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

Step 2

Write the expression using exponents.

Multiply $10$ by $10$ .

$\sqrt[4]{100}$

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

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

Step 3

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

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

Step 4

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

$\sqrt{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$