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

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

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

The square of \sqrt{2} is 2.

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

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

$$\sqrt{2}$$