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

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

Evaluate

$$\frac{\sqrt{6}}{2}+\sqrt{2}\approx 2.638958434$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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