Solve sqrt{(2-2/5)2/5}

$$\sqrt { ( 2 - \frac { 2 } { 5 } ) \frac { 2 } { 5 } }$$

Evaluate

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

Solution Steps

Convert 2 to fraction \frac{10}{5}.

$$\sqrt{\left(\frac{10}{5}-\frac{2}{5}\right)\times \frac{2}{5}}$$

Since \frac{10}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 10 to get 8.

$$\sqrt{\frac{8}{5}\times \frac{2}{5}}$$

Multiply \frac{8}{5} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{8\times 2}{5\times 5}}$$

Do the multiplications in the fraction \frac{8\times 2}{5\times 5}.

$$\sqrt{\frac{16}{25}}$$

Rewrite the square root of the division \frac{16}{25} as the division of square roots \frac{\sqrt{16}}{\sqrt{25}}. Take the square root of both numerator and denominator.

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

Factor

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