Solve sqrt{1/2}*frac{sqrt{2}}{sqrt{2}}

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

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

Divide \sqrt{2} by \sqrt{2} to get 1.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Express \frac{\sqrt{2}}{2}\times 1 as a single fraction.

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