Solve sqrt{1/2}+1/1

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

Evaluate

$$\frac{\sqrt{2}}{2}+1\approx 1.707106781$$

Solution Steps

Divide 1 by 1 to get 1.

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

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

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

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

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