Solve sqrt{20}*sqrt{1/5}=

$$\sqrt { 20 } \times \sqrt { \frac { 1 } { 5 } } =$$

Evaluate

$$2$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{5} is 5.

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

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

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

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

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

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

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

Cancel out 5 and 5.

$$2$$

Factor

$$2$$