Solve sqrt{5/3}+sqrt{3/5}

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

Evaluate

$$\frac{8\sqrt{15}}{15}\approx 2.065591118$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

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

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

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

The square of \sqrt{3} is 3.

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

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

$$\frac{\sqrt{15}}{3}+\sqrt{\frac{3}{5}}$$

Rewrite the square root of the division \sqrt{\frac{3}{5}} as the division of square roots \frac{\sqrt{3}}{\sqrt{5}}.

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{3}}{\sqrt{5}}$$

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

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{3}\sqrt{5}}{5}$$

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

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{15}}{5}$$

Combine \frac{\sqrt{15}}{3} and \frac{\sqrt{15}}{5} to get \frac{8}{15}\sqrt{15}.

$$\frac{8}{15}\sqrt{15}$$