Solve (2)2sqrt{6}*3sqrt{1/2}divsqrt{3}

$$( 2 ) 2 \sqrt { 6 } \times 3 \sqrt { \frac { 1 } { 2 } } \div \sqrt { 3 }$$

Evaluate

$$12$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6\times 2\sqrt{6}\sqrt{\frac{1}{2}}}{\sqrt{3}}$$

Multiply 6 and 2 to get 12.

$$\frac{12\sqrt{6}\sqrt{\frac{1}{2}}}{\sqrt{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{12\sqrt{6}\times \frac{\sqrt{1}}{\sqrt{2}}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$\frac{12\sqrt{6}\times \frac{1}{\sqrt{2}}}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{12\sqrt{6}\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{\sqrt{3}}$$

The square of \sqrt{2} is 2.

$$\frac{12\sqrt{6}\times \frac{\sqrt{2}}{2}}{\sqrt{3}}$$

Cancel out 2, the greatest common factor in 12 and 2.

$$\frac{6\sqrt{2}\sqrt{6}}{\sqrt{3}}$$

Rationalize the denominator of \frac{6\sqrt{2}\sqrt{6}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{6\sqrt{2}\sqrt{6}\sqrt{3}}{3}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$\frac{6\sqrt{2}\sqrt{2}\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{6\times 2\sqrt{3}\sqrt{3}}{3}$$

Multiply 6 and 2 to get 12.

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

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

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

Multiply 12 and 3 to get 36.

$$\frac{36}{3}$$

Divide 36 by 3 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$