Solve sqrt{4/3+125}

$$\sqrt { \frac { 4 } { 3 } + 125 }$$

Evaluate

$$\frac{\sqrt{1137}}{3}\approx 11.2398102$$

Solution Steps

Convert 125 to fraction \frac{375}{3}.

$$\sqrt{\frac{4}{3}+\frac{375}{3}}$$

Since \frac{4}{3} and \frac{375}{3} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{4+375}{3}}$$

Add 4 and 375 to get 379.

$$\sqrt{\frac{379}{3}}$$

Rewrite the square root of the division \sqrt{\frac{379}{3}} as the division of square roots \frac{\sqrt{379}}{\sqrt{3}}.

$$\frac{\sqrt{379}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{379}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{379}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{379}\sqrt{3}}{3}$$

To multiply \sqrt{379} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{1137}}{3}$$