Solve -sqrt{10/25}=

$$- \sqrt { \frac { 10 } { 25 } } =$$

Evaluate

$$-\frac{\sqrt{10}}{5}\approx -0.632455532$$

Solution Steps

Reduce the fraction \frac{10}{25} to lowest terms by extracting and canceling out 5.

$$-\sqrt{\frac{2}{5}}$$

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

$$-\frac{\sqrt{2}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

$$-\frac{\sqrt{2}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$-\frac{\sqrt{10}}{5}$$