Solve 1*1/sqrt{6}+1/sqrt{2}

$$1 \cdot \frac { 1 } { \sqrt { 6 } } + \frac { 1 } { \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{6}+3\sqrt{2}}{6}\approx 1.115355072$$

Short Solution Steps

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

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

The square of \sqrt{6} is 6.

$$1\times \frac{\sqrt{6}}{6}+\frac{1}{\sqrt{2}}$$

Express 1\times \frac{\sqrt{6}}{6} as a single fraction.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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