Solve sqrt{4+2/3}

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

Evaluate

$$\frac{\sqrt{42}}{3}\approx 2.160246899$$

Solution Steps

Convert 4 to fraction \frac{12}{3}.

$$\sqrt{\frac{12}{3}+\frac{2}{3}}$$

Since \frac{12}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{12+2}{3}}$$

Add 12 and 2 to get 14.

$$\sqrt{\frac{14}{3}}$$

Rewrite the square root of the division \sqrt{\frac{14}{3}} as the division of square roots \frac{\sqrt{14}}{\sqrt{3}}.

$$\frac{\sqrt{14}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{14}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{14}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{14}\sqrt{3}}{3}$$

To multiply \sqrt{14} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{42}}{3}$$