Divide ( square root of 15)/(5 square root of 20)

$\frac{\sqrt{15}}{5 \sqrt{20}}$

Combine $\sqrt{15}$ and $\sqrt{20}$ into a single radical.

$\frac{\sqrt{\frac{15}{20}}}{5}$

Cancel the common factor of $15$ and $20$ .

Factor $5$ out of $15$ .

$\frac{\sqrt{\frac{5 (3)}{20}}}{5}$

Cancel the common factors.

Factor $5$ out of $20$ .

$\frac{\sqrt{\frac{5 \cdot 3}{5 \cdot 4}}}{5}$

Cancel the common factor.

$\frac{\sqrt{\frac{5 \cdot 3}{5 \cdot 4}}}{5}$

Rewrite the expression.

$\frac{\sqrt{\frac{3}{4}}}{5}$

Simplify the numerator.

Rewrite $\sqrt{\frac{3}{4}}$ as $\frac{\sqrt{3}}{\sqrt{4}}$ .

$\frac{\frac{\sqrt{3}}{\sqrt{4}}}{5}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$\frac{\frac{\sqrt{3}}{\sqrt{2^{2}}}}{5}$

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

$\frac{\frac{\sqrt{3}}{2}}{5}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{\sqrt{3}}{2} \cdot \frac{1}{5}$

Multiply $\frac{\sqrt{3}}{2} \cdot \frac{1}{5}$ .

Multiply $\frac{\sqrt{3}}{2}$ by $\frac{1}{5}$ .

$\frac{\sqrt{3}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$\frac{\sqrt{3}}{10}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{10}$

Decimal Form:

$0.17320508 \dots$