Solve 3sqrt{2}div2sqrt{6}

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

Evaluate

$$3\sqrt{3}\approx 5.196152423$$

Solution Steps

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

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

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}.

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

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

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

Multiply 3 and 2 to get 6.

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

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

$$3\sqrt{3}$$