Solve sqrt{2}*(-3sqrt{6})*1/2sqrt{3}

$$\sqrt { 2 } \times ( - 3 \sqrt { 6 } ) \times \frac { 1 } { 2 } \sqrt { 3 }$$

Evaluate

$$-9$$

Solution Steps

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}.

$$\sqrt{2}\left(-3\right)\sqrt{2}\sqrt{3}\times \frac{1}{2}\sqrt{3}$$

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

$$2\left(-3\right)\sqrt{3}\times \frac{1}{2}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\left(-3\right)\times 3\times \frac{1}{2}$$

Multiply 2 and -3 to get -6.

$$-6\times 3\times \frac{1}{2}$$

Multiply -6 and 3 to get -18.

$$-18\times \frac{1}{2}$$

Multiply -18 and \frac{1}{2} to get \frac{-18}{2}.

$$\frac{-18}{2}$$

Divide -18 by 2 to get -9.

$$-9$$

Factor

$$-9$$