Solve 50/1-sqrt{3/3}

$$\frac { 50 } { 1 - \frac { \sqrt { 3 } } { 3 } }$$

Evaluate

$$25\sqrt{3}+75\approx 118.301270189$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

$$\frac{50}{\frac{3}{3}-\frac{\sqrt{3}}{3}}$$

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

$$\frac{50}{\frac{3-\sqrt{3}}{3}}$$

Divide 50 by \frac{3-\sqrt{3}}{3} by multiplying 50 by the reciprocal of \frac{3-\sqrt{3}}{3}.

$$\frac{50\times 3}{3-\sqrt{3}}$$

Rationalize the denominator of \frac{50\times 3}{3-\sqrt{3}} by multiplying numerator and denominator by 3+\sqrt{3}.

$$\frac{50\times 3\left(3+\sqrt{3}\right)}{\left(3-\sqrt{3}\right)\left(3+\sqrt{3}\right)}$$

Consider \left(3-\sqrt{3}\right)\left(3+\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{50\times 3\left(3+\sqrt{3}\right)}{3^{2}-\left(\sqrt{3}\right)^{2}}$$

Square 3. Square \sqrt{3}.

$$\frac{50\times 3\left(3+\sqrt{3}\right)}{9-3}$$

Subtract 3 from 9 to get 6.

$$\frac{50\times 3\left(3+\sqrt{3}\right)}{6}$$

Multiply 50 and 3 to get 150.

$$\frac{150\left(3+\sqrt{3}\right)}{6}$$

Divide 150\left(3+\sqrt{3}\right) by 6 to get 25\left(3+\sqrt{3}\right).

$$25\left(3+\sqrt{3}\right)$$

Use the distributive property to multiply 25 by 3+\sqrt{3}.

$$75+25\sqrt{3}$$