# How do you evaluate 3\sqrt { - 24} * 2\sqrt { - 18}?

May 11, 2017

Use $i = \sqrt{- 1}$ and then simplify. Answer: $- 72 \sqrt{3}$

#### Explanation:

Original question: Evaluate $3 \sqrt{- 24} \cdot 2 \sqrt{- 18}$

Since we cannot square root a negative (we CANNOT simply multiplying the square roots together to make the number inside the square root positive), we use the imaginary unit $i = \sqrt{- 1}$ to denote the imaginary unit:

$3 \sqrt{- 24} \cdot 2 \sqrt{- 18}$
$= 3 i \sqrt{24} \cdot 2 i \sqrt{18}$
$= 6 {i}^{2} \sqrt{24 \cdot 18}$
$= 6 {i}^{2} \sqrt{{2}^{3} \cdot 3 \cdot 2 \cdot {3}^{2}}$
$= 6 {i}^{2} \sqrt{{2}^{4} \cdot {3}^{3}}$
$= 6 {i}^{2} \cdot {2}^{2} \cdot 3 \sqrt{3}$

Note that ${i}^{2} = - 1$
$= - 72 \sqrt{3}$