Solve sqrt{16+9/2}

$$\sqrt { 16 + \frac { 9 } { 2 } }$$

Evaluate

$$\frac{\sqrt{82}}{2}\approx 4.527692569$$

Solution Steps

Convert 16 to fraction \frac{32}{2}.

$$\sqrt{\frac{32}{2}+\frac{9}{2}}$$

Since \frac{32}{2} and \frac{9}{2} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{32+9}{2}}$$

Add 32 and 9 to get 41.

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

Rewrite the square root of the division \sqrt{\frac{41}{2}} as the division of square roots \frac{\sqrt{41}}{\sqrt{2}}.

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

Rationalize the denominator of \frac{\sqrt{41}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{41}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

To multiply \sqrt{41} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{82}}{2}$$