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

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

Evaluate

$$2$$

Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

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

The square of \sqrt{2} is 2.

$$2$$

Factor

$$2$$