Solve frac{sqrt{2}+1/sqrt{2}}{sqrt{2}}

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

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Combine \sqrt{2} and \frac{\sqrt{2}}{2} to get \frac{3}{2}\sqrt{2}.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{\frac{3}{2}\times 2}{2}$$

Cancel out 2 and 2.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$