Solve sqrt{7/5*6}

$$\sqrt{ \frac{ 7 }{ 5 \times 6 } }$$

Evaluate

$$\frac{\sqrt{210}}{30}\approx 0.483045892$$

Solution Steps

Multiply 5 and 6 to get 30.

$$\sqrt{\frac{7}{30}}$$

Rewrite the square root of the division \sqrt{\frac{7}{30}} as the division of square roots \frac{\sqrt{7}}{\sqrt{30}}.

$$\frac{\sqrt{7}}{\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{\sqrt{7}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{\sqrt{7}\sqrt{30}}{30}$$

To multiply \sqrt{7} and \sqrt{30}, multiply the numbers under the square root.

$$\frac{\sqrt{210}}{30}$$