Solve sqrt{9/2}+1/2

$$\sqrt { \frac { 9 } { 2 } } + \frac { 1 } { 2 }$$

Evaluate

$$\frac{3\sqrt{2}+1}{2}\approx 2.621320344$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{9}{2}} as the division of square roots \frac{\sqrt{9}}{\sqrt{2}}.

$$\frac{\sqrt{9}}{\sqrt{2}}+\frac{1}{2}$$

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{2}}+\frac{1}{2}$$

Rationalize the denominator of \frac{3}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\frac{1}{2}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{2}+\frac{1}{2}$$

Since \frac{3\sqrt{2}}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{2}+1}{2}$$

Factor

$$\frac{3 \sqrt{2} + 1}{2} = 2.621320343559643$$