Solve frac{sqrt{3}}{sqrt{5}}*5

$$\frac { \sqrt { 3 } } { \sqrt { 5 } } \times 5$$

Evaluate

$$\sqrt{15}\approx 3.872983346$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$5\times \frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$5\times \frac{\sqrt{3}\sqrt{5}}{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$5\times \frac{\sqrt{15}}{5}$$

Cancel out 5 and 5.

$$\sqrt{15}$$