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

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

Evaluate

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

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{\sqrt{5}\times 2\sqrt{2}}{\sqrt{20}}$$

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

$$\frac{\sqrt{10}\times 2}{\sqrt{20}}$$

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}.

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

Cancel out 2 in both numerator and denominator.

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

Rewrite the division of square roots \frac{\sqrt{10}}{\sqrt{5}} as the square root of the division \sqrt{\frac{10}{5}} and perform the division.

$$\sqrt{2}$$