Solve sqrt{12}divfrac{sqrt{3}}{2}

$$\sqrt { 12 } \div \frac { \sqrt { 3 } } { 2 }$$

Evaluate

$$4$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Divide 2\sqrt{3} by \frac{\sqrt{3}}{2} by multiplying 2\sqrt{3} by the reciprocal of \frac{\sqrt{3}}{2}.

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

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

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{4\times 3}{3}$$

Multiply 4 and 3 to get 12.

$$\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$4$$

Factor

$$2^{2}$$