Evaluate ( square root of 15)/( square root of 60)

$\frac{\sqrt{15}}{\sqrt{60}}$

Step 1

Combine $\sqrt{15}$ and $\sqrt{60}$ into a single radical.

$\sqrt{\frac{15}{60}}$

Step 2

Cancel the common factor of $15$ and $60$ .

Factor $15$ out of $15$ .

$\sqrt{\frac{15 (1)}{60}}$

Cancel the common factors.

Factor $15$ out of $60$ .

$\sqrt{\frac{15 \cdot 1}{15 \cdot 4}}$

Cancel the common factor.

$\sqrt{\frac{15 \cdot 1}{15 \cdot 4}}$

Rewrite the expression.

$\sqrt{\frac{1}{4}}$

Step 3

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$\frac{\sqrt{1}}{\sqrt{4}}$

Step 4

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{4}}$

Step 5

Simplify the denominator.

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

$\frac{1}{\sqrt{2^{2}}}$

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

$\frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$