Solve 3sqrt{6}div4sqrt{2}

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

Evaluate

$$\frac{3\sqrt{3}}{2}\approx 2.598076211$$

Solution Steps

Express \frac{3\sqrt{6}}{4}\sqrt{2} as a single fraction.

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

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 3 and 2 to get 6.

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

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

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