Solve frac{sqrt{2}-1+sqrt{6}}{sqrt{5}}

$$\frac { \sqrt { 2 } - 1 + \sqrt { 6 } } { \sqrt { 5 } }$$

Evaluate

$$\frac{\sqrt{5}\left(\sqrt{2}+\sqrt{6}-1\right)}{5}\approx 1.280687052$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{2}-1+\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\left(\sqrt{2}-1+\sqrt{6}\right)\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\left(\sqrt{2}-1+\sqrt{6}\right)\sqrt{5}}{5}$$

Use the distributive property to multiply \sqrt{2}-1+\sqrt{6} by \sqrt{5}.

$$\frac{\sqrt{2}\sqrt{5}-\sqrt{5}+\sqrt{6}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{10}-\sqrt{5}+\sqrt{6}\sqrt{5}}{5}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{10}-\sqrt{5}+\sqrt{30}}{5}$$