Solve sqrt{4/3}+2sqrt{1/3}

$$\sqrt { \frac { 4 } { 3 } } + 2 \sqrt { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{4\sqrt{3}}{3}\approx 2.309401077$$

Solution Steps

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

$$\frac{\sqrt{4}}{\sqrt{3}}+2\sqrt{\frac{1}{3}}$$

Calculate the square root of 4 and get 2.

$$\frac{2}{\sqrt{3}}+2\sqrt{\frac{1}{3}}$$

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

$$\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+2\sqrt{\frac{1}{3}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{3}}{3}+2\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{2\sqrt{3}}{3}+2\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$\frac{2\sqrt{3}}{3}+2\times \frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Express 2\times \frac{\sqrt{3}}{3} as a single fraction.

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

Combine \frac{2\sqrt{3}}{3} and \frac{2\sqrt{3}}{3} to get \frac{4}{3}\sqrt{3}.

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