Solve =4000-40000/sqrt{3}

$$= 4000 - \frac { 40000 } { \sqrt { 3 } }$$

Evaluate

$$-\frac{40000\sqrt{3}}{3}+4000\approx -19094.010767585$$

Short Solution Steps

Rationalize the denominator of \frac{40000}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$4000-\frac{40000\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4000-\frac{40000\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4000 times \frac{3}{3}.

$$\frac{4000\times 3}{3}-\frac{40000\sqrt{3}}{3}$$

Since \frac{4000\times 3}{3} and \frac{40000\sqrt{3}}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4000\times 3-40000\sqrt{3}}{3}$$

Do the multiplications in 4000\times 3-40000\sqrt{3}.

$$\frac{12000-40000\sqrt{3}}{3}$$

Factor

$$\frac{4000 \sqrt{3} {(\sqrt{3} - 10)}}{3} = -19094.01076758503$$