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

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

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

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}.

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

Express 2\times \frac{3}{4} as a single fraction.

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

Multiply 2 and 3 to get 6.

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

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

Divide \frac{3}{2}\sqrt{3} by 3 to get \frac{1}{2}\sqrt{3}.

$$\frac{1}{2}\sqrt{3}\sqrt{2}$$

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

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