Solve afrac{sqrt{3}}{sqrt{5}}

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

Evaluate

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

Solution Steps

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

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

The square of \sqrt{5} is 5.

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

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

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

Express a\times \frac{\sqrt{15}}{5} as a single fraction.

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

Differentiate w.r.t. a

$$\frac{\sqrt{15}}{5} = 0.7745966692414834$$