Solve (-5sqrt{(2/5)+0.8^2}

$$( - 5 \sqrt { ( \frac { 2 } { 5 } ) + 0.8 ^ { 2 } }$$

Evaluate

$$-\sqrt{26}\approx -5.099019514$$

Solution Steps

Calculate 0.8 to the power of 2 and get 0.64.

$$-5\sqrt{\frac{2}{5}+0.64}$$

Convert decimal number 0.64 to fraction \frac{64}{100}. Reduce the fraction \frac{64}{100} to lowest terms by extracting and canceling out 4.

$$-5\sqrt{\frac{2}{5}+\frac{16}{25}}$$

Least common multiple of 5 and 25 is 25. Convert \frac{2}{5} and \frac{16}{25} to fractions with denominator 25.

$$-5\sqrt{\frac{10}{25}+\frac{16}{25}}$$

Since \frac{10}{25} and \frac{16}{25} have the same denominator, add them by adding their numerators.

$$-5\sqrt{\frac{10+16}{25}}$$

Add 10 and 16 to get 26.

$$-5\sqrt{\frac{26}{25}}$$

Rewrite the square root of the division \sqrt{\frac{26}{25}} as the division of square roots \frac{\sqrt{26}}{\sqrt{25}}.

$$-5\times \frac{\sqrt{26}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$-5\times \frac{\sqrt{26}}{5}$$

Cancel out 5 and 5.

$$-\sqrt{26}$$