Solve sqrt{3}+sqrt{16/3}=

$$\sqrt { 3 } + \sqrt { \frac { 16 } { 3 } } =$$

Evaluate

$$\frac{7\sqrt{3}}{3}\approx 4.041451884$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{16}{3}} as the division of square roots \frac{\sqrt{16}}{\sqrt{3}}.

$$\sqrt{3}+\frac{\sqrt{16}}{\sqrt{3}}$$

Calculate the square root of 16 and get 4.

$$\sqrt{3}+\frac{4}{\sqrt{3}}$$

Rationalize the denominator of \frac{4}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\sqrt{3}+\frac{4\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{3}+\frac{4\sqrt{3}}{3}$$

Combine \sqrt{3} and \frac{4\sqrt{3}}{3} to get \frac{7}{3}\sqrt{3}.

$$\frac{7}{3}\sqrt{3}$$