Solve sqrt{5}*sqrt{8/20}

$$\sqrt { 5 } \times \sqrt { \frac { 8 } { 20 } }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Reduce the fraction \frac{8}{20} to lowest terms by extracting and canceling out 4.

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

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

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

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

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

The square of \sqrt{5} is 5.

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

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

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

Express \sqrt{5}\times \frac{\sqrt{10}}{5} as a single fraction.

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

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

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

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

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

Cancel out 5 and 5.

$$\sqrt{2}$$