Solve -100*0.2+2002/sqrt{13}0.3

$$-100 \cdot 0.2+200 \frac{ 2 }{ \sqrt{ 13 } } 0.3$$

Evaluate

$$\frac{120\sqrt{13}}{13}-20\approx 13.282011774$$

Short Solution Steps

Multiply -100 and 0.2 to get -20.

$$-20+0.3\times 200\times \frac{2}{\sqrt{13}}$$

Multiply 0.3 and 200 to get 60.

$$-20+60\times \frac{2}{\sqrt{13}}$$

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

$$-20+60\times \frac{2\sqrt{13}}{\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$-20+60\times \frac{2\sqrt{13}}{13}$$

Express 60\times \frac{2\sqrt{13}}{13} as a single fraction.

$$-20+\frac{60\times 2\sqrt{13}}{13}$$

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

$$-\frac{20\times 13}{13}+\frac{60\times 2\sqrt{13}}{13}$$

Since -\frac{20\times 13}{13} and \frac{60\times 2\sqrt{13}}{13} have the same denominator, add them by adding their numerators.

$$\frac{-20\times 13+60\times 2\sqrt{13}}{13}$$

Do the multiplications in -20\times 13+60\times 2\sqrt{13}.

$$\frac{-260+120\sqrt{13}}{13}$$

Factor

$$\frac{20 {(6 \sqrt{13} - 13)}}{13} = 13.282011773513744$$