Evaluate ( square root of 15)/( square root of 12)

$\frac{\sqrt{15}}{\sqrt{12}}$

Step 1

Combine $\sqrt{15}$ and $\sqrt{12}$ into a single radical.

$\sqrt{\frac{15}{12}}$

Step 2

Cancel the common factor of $15$ and $12$ .

Factor $3$ out of $15$ .

$\sqrt{\frac{3 (5)}{12}}$

Cancel the common factors.

Factor $3$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Rewrite $\sqrt{\frac{5}{4}}$ as $\frac{\sqrt{5}}{\sqrt{4}}$ .

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

Step 4

Simplify the denominator.

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

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

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.11803398 \dots$