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

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

Evaluate

$$-18$$

Solution Steps

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

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

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

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

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

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

Multiply 2 and 3 to get 6.

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

Multiply 6 and 3 to get 18.

$$18\times 2\left(-\frac{1}{2}\right)$$

Multiply 18 and 2 to get 36.

$$36\left(-\frac{1}{2}\right)$$

Express 36\left(-\frac{1}{2}\right) as a single fraction.

$$\frac{36\left(-1\right)}{2}$$

Multiply 36 and -1 to get -36.

$$\frac{-36}{2}$$

Divide -36 by 2 to get -18.

$$-18$$

Factor

$$-18$$