Solve frac{sqrt{3}-3}{sqrt{3}}

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

Evaluate

$$1-\sqrt{3}\approx -0.732050808$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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

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

The square of \sqrt{3} is 3.

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

Divide each term of 3-3\sqrt{3} by 3 to get 1-\sqrt{3}.

$$1-\sqrt{3}$$