Solve frac{6-sqrt{3}}{sqrt{3}}

$$\frac{ 6- \sqrt{ 3 } }{ \sqrt{ 3 } }$$

Evaluate

$$2\sqrt{3}-1\approx 2.464101615$$

Solution Steps

Rationalize the denominator of \frac{6-\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(6-\sqrt{3}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Use the distributive property to multiply 6-\sqrt{3} by \sqrt{3}.

$$\frac{6\sqrt{3}-\left(\sqrt{3}\right)^{2}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{6\sqrt{3}-3}{3}$$

Divide each term of 6\sqrt{3}-3 by 3 to get 2\sqrt{3}-1.

$$2\sqrt{3}-1$$