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

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

Evaluate

$$\frac{\sqrt{6}-2\sqrt{3}}{12}\approx -0.084550989$$

Solution Steps

Rationalize the denominator of \frac{1-\sqrt{2}}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

Multiply 2 and 6 to get 12.

$$\frac{\left(1-\sqrt{2}\right)\sqrt{6}}{12}$$

Use the distributive property to multiply 1-\sqrt{2} by \sqrt{6}.

$$\frac{\sqrt{6}-\sqrt{2}\sqrt{6}}{12}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$\frac{\sqrt{6}-\sqrt{2}\sqrt{2}\sqrt{3}}{12}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{\sqrt{6}-2\sqrt{3}}{12}$$