Solve sqrt{6}*frac{3sqrt{2}}{2}

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

Evaluate

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

Solution Steps

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

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

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}.

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

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

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

Multiply 2 and 3 to get 6.

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

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

$$3\sqrt{3}$$