Solve sqrt{1/2}-sqrt{1/6}

$$\sqrt { \frac { 1 } { 2 } } - \sqrt { \frac { 1 } { 6 } }$$

Evaluate

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{6}}{6}\approx 0.298858491$$

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}}.

$$\frac{\sqrt{1}}{\sqrt{2}}-\sqrt{\frac{1}{6}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{2}}-\sqrt{\frac{1}{6}}$$

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

$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\sqrt{\frac{1}{6}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}-\sqrt{\frac{1}{6}}$$

Rewrite the square root of the division \sqrt{\frac{1}{6}} as the division of square roots \frac{\sqrt{1}}{\sqrt{6}}.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{1}}{\sqrt{6}}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{2}}{2}-\frac{1}{\sqrt{6}}$$

Rationalize the denominator of \frac{1}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{6}}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 6 is 6. Multiply \frac{\sqrt{2}}{2} times \frac{3}{3}.

$$\frac{3\sqrt{2}}{6}-\frac{\sqrt{6}}{6}$$

Since \frac{3\sqrt{2}}{6} and \frac{\sqrt{6}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\sqrt{2}-\sqrt{6}}{6}$$