Simplify ( square root of 5)/( square root of 45)

$\frac{\sqrt{5}}{\sqrt{45}}$

Step 1

Combine $\sqrt{5}$ and $\sqrt{45}$ into a single radical.

$\sqrt{\frac{5}{45}}$

Step 2

Cancel the common factor of $5$ and $45$ .

Factor $5$ out of $5$ .

$\sqrt{\frac{5 (1)}{45}}$

Cancel the common factors.

Factor $5$ out of $45$ .

$\sqrt{\frac{5 \cdot 1}{5 \cdot 9}}$

Cancel the common factor.

$\sqrt{\frac{5 \cdot 1}{5 \cdot 9}}$

Rewrite the expression.

$\sqrt{\frac{1}{9}}$

Step 3

Rewrite $\sqrt{\frac{1}{9}}$ as $\frac{\sqrt{1}}{\sqrt{9}}$ .

$\frac{\sqrt{1}}{\sqrt{9}}$

Step 4

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{9}}$

Step 5

Simplify the denominator.

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

$\frac{1}{\sqrt{3^{2}}}$

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

$\frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$