Solve sqrt{25/195}=

$$\sqrt{ \frac{ 25 }{ 195 } } =$$

Evaluate

$$\frac{\sqrt{195}}{39}\approx 0.358057437$$

Solution Steps

Reduce the fraction \frac{25}{195} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{5}{39}}$$

Rewrite the square root of the division \sqrt{\frac{5}{39}} as the division of square roots \frac{\sqrt{5}}{\sqrt{39}}.

$$\frac{\sqrt{5}}{\sqrt{39}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{39}} by multiplying numerator and denominator by \sqrt{39}.

$$\frac{\sqrt{5}\sqrt{39}}{\left(\sqrt{39}\right)^{2}}$$

The square of \sqrt{39} is 39.

$$\frac{\sqrt{5}\sqrt{39}}{39}$$

To multiply \sqrt{5} and \sqrt{39}, multiply the numbers under the square root.

$$\frac{\sqrt{195}}{39}$$