Solve sqrt{4/5}*sqrt{2/1}*sqrt{2/5}

$$\sqrt { \frac { 4 } { 5 } } \cdot \sqrt { \frac { 2 } { 1 } } \cdot \sqrt { \frac { 2 } { 5 } }$$

Evaluate

$$\frac{4}{5}=0.8$$

Solution Steps

To multiply \sqrt{\frac{4}{5}} and \sqrt{\frac{2}{5}}, multiply the numbers under the square root.

$$\sqrt{\frac{8}{25}}\sqrt{\frac{2}{1}}$$

Rewrite the square root of the division \sqrt{\frac{8}{25}} as the division of square roots \frac{\sqrt{8}}{\sqrt{25}}.

$$\frac{\sqrt{8}}{\sqrt{25}}\sqrt{\frac{2}{1}}$$

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}.

$$\frac{2\sqrt{2}}{\sqrt{25}}\sqrt{\frac{2}{1}}$$

Calculate the square root of 25 and get 5.

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

Anything divided by one gives itself.

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

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and 2 to get 4.

$$\frac{4}{5}$$

Factor

$$\frac{2 ^ {2}}{5} = 0.8$$