Solve 10sqrt{6/7}

$$10 \sqrt { \frac { 6 } { 7 } }$$

Evaluate

$$\frac{10\sqrt{42}}{7}\approx 9.258200998$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{6}{7}} as the division of square roots \frac{\sqrt{6}}{\sqrt{7}}.

$$10\times \frac{\sqrt{6}}{\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{6}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$10\times \frac{\sqrt{6}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$10\times \frac{\sqrt{6}\sqrt{7}}{7}$$

To multiply \sqrt{6} and \sqrt{7}, multiply the numbers under the square root.

$$10\times \frac{\sqrt{42}}{7}$$

Express 10\times \frac{\sqrt{42}}{7} as a single fraction.

$$\frac{10\sqrt{42}}{7}$$