Solve sqrt{1/2}-1/2sqrt{1/2}

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

Evaluate

$$\frac{\sqrt{2}}{4}\approx 0.353553391$$

Short Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply -\frac{1}{2} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2\times 2 is 2\times 2. Multiply \frac{\sqrt{2}}{2} times \frac{2}{2}.

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

Since \frac{2\sqrt{2}}{2\times 2} and \frac{-\sqrt{2}}{2\times 2} have the same denominator, add them by adding their numerators.

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

Do the calculations in 2\sqrt{2}-\sqrt{2}.

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

Expand 2\times 2.

$$\frac{\sqrt{2}}{4}$$