Solve 6sqrt{27}*(-2sqrt{3})=

$$6 \sqrt { 27 } \times ( - 2 \sqrt { 3 } ) =$$

Evaluate

$$-108$$

Solution Steps

Factor 27=3\times 9. Rewrite the square root of the product \sqrt{3\times 9} as the product of square roots \sqrt{3}\sqrt{9}.

$$6\sqrt{3}\sqrt{9}\left(-2\right)\sqrt{3}$$

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

$$6\times 3\left(-2\right)\sqrt{9}$$

Multiply 6 and 3 to get 18.

$$18\left(-2\right)\sqrt{9}$$

Multiply 18 and -2 to get -36.

$$-36\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$-36\times 3$$

Multiply -36 and 3 to get -108.

$$-108$$

Factor

$$-108$$