Solve sqrt{1/8}-sqrt{6}

$$\sqrt { \frac { 1 } { 8 } } - \sqrt { 6 }$$

Evaluate

$$\frac{\sqrt{2}}{4}-\sqrt{6}\approx -2.095936352$$

Short Solution Steps

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

$$\frac{\sqrt{1}}{\sqrt{8}}-\sqrt{6}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{8}}-\sqrt{6}$$

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}.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{2}}{4}-\sqrt{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{6} times \frac{4}{4}.

$$\frac{\sqrt{2}}{4}-\frac{4\sqrt{6}}{4}$$

Since \frac{\sqrt{2}}{4} and \frac{4\sqrt{6}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{2}-4\sqrt{6}}{4}$$