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

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

Evaluate

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

Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Calculate the square root of 1 and get 1.

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

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}.

$$\sqrt{2}$$