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

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

Evaluate

$$\frac{\sqrt{2}}{2}+\frac{3}{4}\approx 1.457106781$$

Short Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

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{2}}{2} times \frac{2}{2}.

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

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

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

Factor

$$\frac{2 \sqrt{2} + 3}{4} = 1.4571067811865475$$