Solve sqrt{1/2}*sqrt{2/5}*sqrt{5}

$$\sqrt{ \frac{ 1 }{ 2 } } \times \sqrt{ \frac{ 2 }{ 5 } } \times \sqrt{ 5 }$$

Evaluate

$$1$$

Solution Steps

To multiply \sqrt{\frac{1}{2}} and \sqrt{\frac{2}{5}}, multiply the numbers under the square root.

$$\sqrt{\frac{1}{5}}\sqrt{5}$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\frac{\sqrt{1}}{\sqrt{5}}\sqrt{5}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{5}}\sqrt{5}$$

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

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

The square of \sqrt{5} is 5.

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

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

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5}{5}$$

Divide 5 by 5 to get 1.

$$1$$

Factor

$$1$$