Evaluate ( square root of 8)/( square root of 100)

$\frac{\sqrt{8}}{\sqrt{100}}$

Step 1

Combine $\sqrt{8}$ and $\sqrt{100}$ into a single radical.

$\sqrt{\frac{8}{100}}$

Step 2

Cancel the common factor of $8$ and $100$ .

Factor $4$ out of $8$ .

$\sqrt{\frac{4 (2)}{100}}$

Cancel the common factors.

Factor $4$ out of $100$ .

$\sqrt{\frac{4 \cdot 2}{4 \cdot 25}}$

Cancel the common factor.

$\sqrt{\frac{4 \cdot 2}{4 \cdot 25}}$

Rewrite the expression.

$\sqrt{\frac{2}{25}}$

Step 3

Rewrite $\sqrt{\frac{2}{25}}$ as $\frac{\sqrt{2}}{\sqrt{25}}$ .

$\frac{\sqrt{2}}{\sqrt{25}}$

Step 4

Simplify the denominator.

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

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

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

$\frac{\sqrt{2}}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2}}{5}$

Decimal Form:

$0.28284271 \dots$