Solve sqrt{1/2}-sqrt{1/8}

$$\sqrt{ \frac{ 1 }{ 2 } } - \sqrt{ \frac{ 1 }{ 8 } }$$

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}}.

$$\frac{\sqrt{1}}{\sqrt{2}}-\sqrt{\frac{1}{8}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{2}}-\sqrt{\frac{1}{8}}$$

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

$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\sqrt{\frac{1}{8}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}-\sqrt{\frac{1}{8}}$$

Rewrite the square root of the division \sqrt{\frac{1}{8}} as the division of square roots \frac{\sqrt{1}}{\sqrt{8}}.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{1}}{\sqrt{8}}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{2}}{2}-\frac{1}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{\sqrt{2}}{2} times \frac{2}{2}.

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

Since \frac{2\sqrt{2}}{4} and \frac{\sqrt{2}}{4} have the same denominator, subtract them by subtracting their numerators.

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

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

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