Solve sqrt{9+12+27/4}

$$\sqrt { 9 + 12 + \frac { 27 } { 4 } }$$

Evaluate

$$\frac{\sqrt{111}}{2}\approx 5.267826876$$

Solution Steps

Add 9 and 12 to get 21.

$$\sqrt{21+\frac{27}{4}}$$

Convert 21 to fraction \frac{84}{4}.

$$\sqrt{\frac{84}{4}+\frac{27}{4}}$$

Since \frac{84}{4} and \frac{27}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{84+27}{4}}$$

Add 84 and 27 to get 111.

$$\sqrt{\frac{111}{4}}$$

Rewrite the square root of the division \sqrt{\frac{111}{4}} as the division of square roots \frac{\sqrt{111}}{\sqrt{4}}.

$$\frac{\sqrt{111}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{111}}{2}$$