Solve sqrt{200/240}

$$\sqrt { \frac { 200 } { 240 } }$$

Evaluate

$$\frac{\sqrt{30}}{6}\approx 0.912870929$$

Solution Steps

Reduce the fraction \frac{200}{240} to lowest terms by extracting and canceling out 40.

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

Rewrite the square root of the division \sqrt{\frac{5}{6}} as the division of square roots \frac{\sqrt{5}}{\sqrt{6}}.

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

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{6}$$