Solve sqrt{265/25}

$$\sqrt { \frac { 265 } { 25 } }$$

Evaluate

$$\frac{\sqrt{265}}{5}\approx 3.255764119$$

Solution Steps

Reduce the fraction \frac{265}{25} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{53}{5}}$$

Rewrite the square root of the division \sqrt{\frac{53}{5}} as the division of square roots \frac{\sqrt{53}}{\sqrt{5}}.

$$\frac{\sqrt{53}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{53}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{53}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{53}\sqrt{5}}{5}$$

To multiply \sqrt{53} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{265}}{5}$$