Solve frac{sqrt{2}}{2}divsqrt{5}

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

Evaluate

$$\frac{\sqrt{10}}{10}\approx 0.316227766$$

Solution Steps

Express \frac{\frac{\sqrt{2}}{2}}{\sqrt{5}} as a single fraction.

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

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

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

The square of \sqrt{5} is 5.

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

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

$$\frac{\sqrt{10}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{10}}{10}$$