Solve sqrt{4/3}+2

$$\sqrt { \frac { 4 } { 3 } } + 2$$

Evaluate

$$\frac{2\sqrt{3}}{3}+2\approx 3.154700538$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{4}{3}} as the division of square roots \frac{\sqrt{4}}{\sqrt{3}}.

$$\frac{\sqrt{4}}{\sqrt{3}}+2$$

Calculate the square root of 4 and get 2.

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

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

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

The square of \sqrt{3} is 3.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{3}{3}.

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

Since \frac{2\sqrt{3}}{3} and \frac{2\times 3}{3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\sqrt{3}+2\times 3.

$$\frac{2\sqrt{3}+6}{3}$$