Solve frac{1+sqrt{3}}{sqrt{2}}

$$\frac { 1 + \sqrt { 3 } } { \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{2}\left(\sqrt{3}+1\right)}{2}\approx 1.931851653$$

Solution Steps

Rationalize the denominator of \frac{1+\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(1+\sqrt{3}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(1+\sqrt{3}\right)\sqrt{2}}{2}$$

Use the distributive property to multiply 1+\sqrt{3} by \sqrt{2}.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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