Solve 2sqrt{12}*3/4div3sqrt{2}

$$2 \sqrt{ 12 } \times \frac{ 3 }{ 4 } \div 3 \sqrt{ 2 }$$

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

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

Cancel out 4 and 4.

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

Cancel out 3 and 3.

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

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

$$\sqrt{6}$$