Evaluate square root of 8/18

$\sqrt{\frac{8}{18}}$

Step 1

Cancel the common factor of $8$ and $18$ .

Factor $2$ out of $8$ .

$\sqrt{\frac{2 (4)}{18}}$

Cancel the common factors.

Factor $2$ out of $18$ .

$\sqrt{\frac{2 \cdot 4}{2 \cdot 9}}$

Cancel the common factor.

$\sqrt{\frac{2 \cdot 4}{2 \cdot 9}}$

Rewrite the expression.

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

Step 2

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

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

Step 3

Simplify the numerator.

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

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

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

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

Step 4

Simplify the denominator.

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

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

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

$\frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$