Solve sqrt{5/3}+sqrt{5/12}

$$\sqrt { \frac { 5 } { 3 } } + \sqrt { \frac { 5 } { 12 } }$$

Evaluate

$$\frac{\sqrt{15}}{2}\approx 1.936491673$$

Solution Steps

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

$$\frac{\sqrt{5}}{\sqrt{3}}+\sqrt{\frac{5}{12}}$$

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

$$\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{\frac{5}{12}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{5}\sqrt{3}}{3}+\sqrt{\frac{5}{12}}$$

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

$$\frac{\sqrt{15}}{3}+\sqrt{\frac{5}{12}}$$

Rewrite the square root of the division \sqrt{\frac{5}{12}} as the division of square roots \frac{\sqrt{5}}{\sqrt{12}}.

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{5}}{\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{5}}{2\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{5}}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{5}\sqrt{3}}{2\times 3}$$

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

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{15}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{15}}{3}+\frac{\sqrt{15}}{6}$$

Combine \frac{\sqrt{15}}{3} and \frac{\sqrt{15}}{6} to get \frac{1}{2}\sqrt{15}.

$$\frac{1}{2}\sqrt{15}$$