Solve 12/sqrt{6}*12/sqrt{2}*1/2

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

Evaluate

$$12\sqrt{3}\approx 20.784609691$$

Solution Steps

Rationalize the denominator of \frac{12}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{12\sqrt{6}}{\left(\sqrt{6}\right)^{2}}\times \frac{12}{\sqrt{2}}\times \frac{1}{2}$$

The square of \sqrt{6} is 6.

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

Divide 12\sqrt{6} by 6 to get 2\sqrt{6}.

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

Rationalize the denominator of \frac{12}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$2\sqrt{6}\times \frac{12\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{1}{2}$$

The square of \sqrt{2} is 2.

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

Divide 12\sqrt{2} by 2 to get 6\sqrt{2}.

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

Multiply 2 and 6 to get 12.

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

Multiply 12 and \frac{1}{2} to get \frac{12}{2}.

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

Divide 12 by 2 to get 6.

$$6\sqrt{6}\sqrt{2}$$

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}.

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

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

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

Multiply 6 and 2 to get 12.

$$12\sqrt{3}$$