Solve sqrt{1/2}*(sqrt{2})^2

$$\sqrt { \frac { 1 } { 2 } } \times ( \sqrt { 2 } ) ^ { 2 }$$

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}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}\times 2$$

Cancel out 2 and 2.

$$\sqrt{2}$$