Simplify (3 square root of 20)/( square root of 45)

$\frac{3 \sqrt{20}}{\sqrt{45}}$

Combine $\sqrt{20}$ and $\sqrt{45}$ into a single radical.

$3 \sqrt{\frac{20}{45}}$

Cancel the common factor of $20$ and $45$ .

Factor $5$ out of $20$ .

$3 \sqrt{\frac{5 (4)}{45}}$

Cancel the common factors.

Factor $5$ out of $45$ .

$3 \sqrt{\frac{5 \cdot 4}{5 \cdot 9}}$

Cancel the common factor.

$3 \sqrt{\frac{5 \cdot 4}{5 \cdot 9}}$

Rewrite the expression.

$3 \sqrt{\frac{4}{9}}$

Rewrite $\sqrt{\frac{4}{9}}$ as $\frac{\sqrt{4}}{\sqrt{9}}$ .

$3 \frac{\sqrt{4}}{\sqrt{9}}$

Simplify the numerator.

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

$3 \frac{\sqrt{2^{2}}}{\sqrt{9}}$

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

$3 \frac{2}{\sqrt{9}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

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

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

$3 (\frac{2}{3})$

Cancel the common factor of $3$ .

Cancel the common factor.

$3 (\frac{2}{3})$

Rewrite the expression.

$2$