Solve 200(frac{sqrt{3}+1}{sqrt{3}})

$$200 ( \frac { \sqrt { 3 } + 1 } { \sqrt { 3 } } )$$

Evaluate

$$\frac{200\sqrt{3}}{3}+200\approx 315.470053838$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{3}+1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$200\times \frac{\left(\sqrt{3}+1\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$200\times \frac{\left(\sqrt{3}+1\right)\sqrt{3}}{3}$$

Express 200\times \frac{\left(\sqrt{3}+1\right)\sqrt{3}}{3} as a single fraction.

$$\frac{200\left(\sqrt{3}+1\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 200 by \sqrt{3}+1.

$$\frac{\left(200\sqrt{3}+200\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 200\sqrt{3}+200 by \sqrt{3}.

$$\frac{200\left(\sqrt{3}\right)^{2}+200\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{200\times 3+200\sqrt{3}}{3}$$

Multiply 200 and 3 to get 600.

$$\frac{600+200\sqrt{3}}{3}$$