Solve 2+frac{sqrt{3}}{sqrt{5}}

$$2+ \frac{ \sqrt{ 3 } }{ \sqrt{ 5 } }$$

Evaluate

$$\frac{\sqrt{15}}{5}+2\approx 2.774596669$$

Short Solution Steps

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

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

The square of \sqrt{5} is 5.

$$2+\frac{\sqrt{3}\sqrt{5}}{5}$$

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

$$2+\frac{\sqrt{15}}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5}{5}.

$$\frac{2\times 5}{5}+\frac{\sqrt{15}}{5}$$

Since \frac{2\times 5}{5} and \frac{\sqrt{15}}{5} have the same denominator, add them by adding their numerators.

$$\frac{2\times 5+\sqrt{15}}{5}$$

Do the multiplications in 2\times 5+\sqrt{15}.

$$\frac{10+\sqrt{15}}{5}$$