Solve sqrt{3/2}-1/4+1

$$\sqrt { \frac { 3 } { 2 } } - \frac { 1 } { 4 } + 1$$

Evaluate

$$\frac{\sqrt{6}}{2}+\frac{3}{4}\approx 1.974744871$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$\frac{\sqrt{3}}{\sqrt{2}}-\frac{1}{4}+1$$

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

$$\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{1}{4}+1$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{2}-\frac{1}{4}+1$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{2}-\frac{1}{4}+1$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\sqrt{6}}{2}-\frac{1}{4}+\frac{4}{4}$$

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

$$\frac{\sqrt{6}}{2}+\frac{-1+4}{4}$$

Add -1 and 4 to get 3.

$$\frac{\sqrt{6}}{2}+\frac{3}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{\sqrt{6}}{2} times \frac{2}{2}.

$$\frac{2\sqrt{6}}{4}+\frac{3}{4}$$

Since \frac{2\sqrt{6}}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2\sqrt{6}+3}{4}$$

Factor

$$\frac{2 \sqrt{6} + 3}{4} = 1.974744871391589$$