Solve -100*0.2-3002/sqrt{13}0.1

$$-100 \cdot 0.2-300 \frac{ 2 }{ \sqrt{ 13 } } 0.1$$

Evaluate

$$-\frac{60\sqrt{13}}{13}-20\approx -36.641005887$$

Short Solution Steps

Multiply -100 and 0.2 to get -20.

$$-20-0.1\times 300\times \frac{2}{\sqrt{13}}$$

Multiply 0.1 and 300 to get 30.

$$-20-30\times \frac{2}{\sqrt{13}}$$

Rationalize the denominator of \frac{2}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$-20-30\times \frac{2\sqrt{13}}{\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$-20-30\times \frac{2\sqrt{13}}{13}$$

Express 30\times \frac{2\sqrt{13}}{13} as a single fraction.

$$-20-\frac{30\times 2\sqrt{13}}{13}$$

Multiply 30 and 2 to get 60.

$$-20-\frac{60\sqrt{13}}{13}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -20 times \frac{13}{13}.

$$-\frac{20\times 13}{13}-\frac{60\sqrt{13}}{13}$$

Since -\frac{20\times 13}{13} and \frac{60\sqrt{13}}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-20\times 13-60\sqrt{13}}{13}$$

Do the multiplications in -20\times 13-60\sqrt{13}.

$$\frac{-260-60\sqrt{13}}{13}$$

Factor

$$\frac{20 {(-3 \sqrt{13} - 13)}}{13} = -36.64100588675687$$