Solve frac{sqrt{2}}{2}*2/sqrt{2}

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

Evaluate

$$1$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

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

Express \frac{\sqrt{2}}{2}\sqrt{2} as a single fraction.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$1$$

Factor

$$1$$