Solve sqrt{16+1/4+9}

$$\sqrt { 16 + \frac { 1 } { 4 } + 9 }$$

Evaluate

$$\frac{\sqrt{101}}{2}\approx 5.024937811$$

Solution Steps

Convert 16 to fraction \frac{64}{4}.

$$\sqrt{\frac{64}{4}+\frac{1}{4}+9}$$

Since \frac{64}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{64+1}{4}+9}$$

Add 64 and 1 to get 65.

$$\sqrt{\frac{65}{4}+9}$$

Convert 9 to fraction \frac{36}{4}.

$$\sqrt{\frac{65}{4}+\frac{36}{4}}$$

Since \frac{65}{4} and \frac{36}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{65+36}{4}}$$

Add 65 and 36 to get 101.

$$\sqrt{\frac{101}{4}}$$

Rewrite the square root of the division \sqrt{\frac{101}{4}} as the division of square roots \frac{\sqrt{101}}{\sqrt{4}}.

$$\frac{\sqrt{101}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{101}}{2}$$