Solve sqrt{25/4+2+2}

$$\sqrt { \frac { 25 } { 4 } + 2 + 2 }$$

Evaluate

$$\frac{\sqrt{41}}{2}\approx 3.201562119$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\sqrt{\frac{25}{4}+\frac{8}{4}+2}$$

Since \frac{25}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{25+8}{4}+2}$$

Add 25 and 8 to get 33.

$$\sqrt{\frac{33}{4}+2}$$

Convert 2 to fraction \frac{8}{4}.

$$\sqrt{\frac{33}{4}+\frac{8}{4}}$$

Since \frac{33}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{33+8}{4}}$$

Add 33 and 8 to get 41.

$$\sqrt{\frac{41}{4}}$$

Rewrite the square root of the division \sqrt{\frac{41}{4}} as the division of square roots \frac{\sqrt{41}}{\sqrt{4}}.

$$\frac{\sqrt{41}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{41}}{2}$$