Solve (sqrt{2}-1)divsqrt{5}

$$( \sqrt { 2 } - 1 ) \div \sqrt { 5 }$$

Evaluate

$$\frac{\sqrt{5}\left(\sqrt{2}-1\right)}{5}\approx 0.185241937$$

Solution Steps

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

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

The square of \sqrt{5} is 5.

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

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

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

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

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