Solve frac{2+sqrt{6}}{sqrt{2}}

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

Evaluate

$$\sqrt{2}+\sqrt{3}\approx 3.14626437$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

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}.

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

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

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

Divide each term of 2\sqrt{2}+2\sqrt{3} by 2 to get \sqrt{2}+\sqrt{3}.

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