Solve 3sqrt{18}*frac{sqrt{3}}{6}div2sqrt{6}

$$3 \sqrt{ 18 } \times \frac{ \sqrt{ 3 } }{ 6 } \div 2 \sqrt{ 6 }$$

Evaluate

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

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{2}\times \frac{\sqrt{3}}{6}}{2}\sqrt{6}$$

Express 9\times \frac{\sqrt{3}}{6} as a single fraction.

$$\frac{\frac{9\sqrt{3}}{6}\sqrt{2}}{2}\sqrt{6}$$

Divide 9\sqrt{3} by 6 to get \frac{3}{2}\sqrt{3}.

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

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

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

Divide \frac{3}{2}\sqrt{6} by 2 to get \frac{3}{4}\sqrt{6}.

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

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

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

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

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

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

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