Solve (3-2sqrt{3})divsqrt{3}

$$(3-2 \sqrt{ 3 } ) \div \sqrt{ 3 }$$

Evaluate

$$\sqrt{3}-2\approx -0.267949192$$

Solution Steps

Rationalize the denominator of \frac{3-2\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Use the distributive property to multiply 3-2\sqrt{3} by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{3\sqrt{3}-2\times 3}{3}$$

Multiply -2 and 3 to get -6.

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

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

$$\sqrt{3}-2$$

Factor

$$\sqrt{3} - 2 = -0.267949192$$