Solve sqrt{9+3/2}

$$\sqrt { 9 + \frac { 3 } { 2 } }$$

Evaluate

$$\frac{\sqrt{42}}{2}\approx 3.240370349$$

Solution Steps

Convert 9 to fraction \frac{18}{2}.

$$\sqrt{\frac{18}{2}+\frac{3}{2}}$$

Since \frac{18}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{18+3}{2}}$$

Add 18 and 3 to get 21.

$$\sqrt{\frac{21}{2}}$$

Rewrite the square root of the division \sqrt{\frac{21}{2}} as the division of square roots \frac{\sqrt{21}}{\sqrt{2}}.

$$\frac{\sqrt{21}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{21}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{21}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{21}\sqrt{2}}{2}$$

To multiply \sqrt{21} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{42}}{2}$$