Solve frac{3*4sqrt{6}}{2sqrt{2}*3sqrt{3}}

$$\frac { 3 \times 4 \sqrt { 6 } } { 2 \sqrt { 2 } \times 3 \sqrt { 3 } }$$

Evaluate

$$2$$

Solution Steps

Cancel out 2\times 3 in both numerator and denominator.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

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

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

The square of \sqrt{6} is 6.

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

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

Multiply 2 and 6 to get 12.

$$\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$2$$

Factor

$$2$$