Simplify (8 square root of 14)/(12 square root of 18)

$\frac{8 \sqrt{14}}{12 \sqrt{18}}$

Cancel the common factor of $8$ and $12$ .

Factor $4$ out of $8 \sqrt{14}$ .

$\frac{4 (2 \sqrt{14})}{12 \sqrt{18}}$

Cancel the common factors.

Factor $4$ out of $12 \sqrt{18}$ .

$\frac{4 (2 \sqrt{14})}{4 (3 \sqrt{18})}$

Cancel the common factor.

$\frac{4 (2 \sqrt{14})}{4 (3 \sqrt{18})}$

Rewrite the expression.

$\frac{2 \sqrt{14}}{3 \sqrt{18}}$

Combine $\sqrt{14}$ and $\sqrt{18}$ into a single radical.

$\frac{2 \sqrt{\frac{14}{18}}}{3}$

Cancel the common factor of $14$ and $18$ .

Factor $2$ out of $14$ .

$\frac{2 \sqrt{\frac{2 (7)}{18}}}{3}$

Cancel the common factors.

Factor $2$ out of $18$ .

$\frac{2 \sqrt{\frac{2 \cdot 7}{2 \cdot 9}}}{3}$

Cancel the common factor.

$\frac{2 \sqrt{\frac{2 \cdot 7}{2 \cdot 9}}}{3}$

Rewrite the expression.

$\frac{2 \sqrt{\frac{7}{9}}}{3}$

Simplify the numerator.

Rewrite $\sqrt{\frac{7}{9}}$ as $\frac{\sqrt{7}}{\sqrt{9}}$ .

$\frac{2 \frac{\sqrt{7}}{\sqrt{9}}}{3}$

Simplify the denominator.

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

$\frac{2 \frac{\sqrt{7}}{\sqrt{3^{2}}}}{3}$

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

$\frac{2 \frac{\sqrt{7}}{3}}{3}$

Combine $2$ and $\frac{\sqrt{7}}{3}$ .

$\frac{\frac{2 \sqrt{7}}{3}}{3}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 \sqrt{7}}{3} \cdot \frac{1}{3}$

Multiply $\frac{2 \sqrt{7}}{3} \cdot \frac{1}{3}$ .

Multiply $\frac{2 \sqrt{7}}{3}$ by $\frac{1}{3}$ .

$\frac{2 \sqrt{7}}{3 \cdot 3}$

Multiply $3$ by $3$ .

$\frac{2 \sqrt{7}}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{7}}{9}$

Decimal Form:

$0.58794473 \dots$