Simplify ( square root of 8)/(2 square root of 9)

$\frac{\sqrt{8}}{2 \sqrt{9}}$

Simplify the numerator.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\frac{\sqrt{4 (2)}}{2 \sqrt{9}}$

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

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

Pull terms out from under the radical.

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

Simplify the denominator.

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

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

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

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

Reduce the expression by cancelling the common factors.

Multiply $2$ by $3$ .

$\frac{2 \sqrt{2}}{6}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2 \sqrt{2}$ .

$\frac{2 (\sqrt{2})}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.47140452 \dots$