Evaluate ( square root of 6)/( square root of 54)

$\frac{\sqrt{6}}{\sqrt{54}}$

Step 1

Combine $\sqrt{6}$ and $\sqrt{54}$ into a single radical.

$\sqrt{\frac{6}{54}}$

Step 2

Cancel the common factor of $6$ and $54$ .

Factor $6$ out of $6$ .

$\sqrt{\frac{6 (1)}{54}}$

Cancel the common factors.

Factor $6$ out of $54$ .

$\sqrt{\frac{6 \cdot 1}{6 \cdot 9}}$

Cancel the common factor.

$\sqrt{\frac{6 \cdot 1}{6 \cdot 9}}$

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:

$0.\overline{3}$