Solve (-5sqrt{(2/5)+08^2}

$$( - 5 \sqrt { ( \frac { 2 } { 5 } ) + 08 ^ { 2 } }$$

Evaluate

$$-\sqrt{1610}\approx -40.124805295$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$-5\sqrt{\frac{2}{5}+64}$$

Convert 64 to fraction \frac{320}{5}.

$$-5\sqrt{\frac{2}{5}+\frac{320}{5}}$$

Since \frac{2}{5} and \frac{320}{5} have the same denominator, add them by adding their numerators.

$$-5\sqrt{\frac{2+320}{5}}$$

Add 2 and 320 to get 322.

$$-5\sqrt{\frac{322}{5}}$$

Rewrite the square root of the division \sqrt{\frac{322}{5}} as the division of square roots \frac{\sqrt{322}}{\sqrt{5}}.

$$-5\times \frac{\sqrt{322}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{322}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$-5\times \frac{\sqrt{322}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$-5\times \frac{\sqrt{322}\sqrt{5}}{5}$$

To multiply \sqrt{322} and \sqrt{5}, multiply the numbers under the square root.

$$-5\times \frac{\sqrt{1610}}{5}$$

Cancel out 5 and 5.

$$-\sqrt{1610}$$