Solve frac{3sqrt{6}}{2}div2sqrt{6}

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

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Express \frac{\frac{3\sqrt{6}}{2}}{2} as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Express \frac{3\sqrt{6}}{4}\sqrt{6} as a single fraction.

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

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

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

Multiply 3 and 6 to get 18.

$$\frac{18}{4}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$