Final answer:
The product of -1.222222... (a rational number) and √ 9 (also a rational number) is rational because the product of two rational numbers is always rational.
Step-by-step explanation:
When considering the product of -1.222222... (which is a repeating decimal and can be expressed as a ratio of integers, hence a rational number) and √ 9 (which is equal to 3, a rational number), we must recognize that the product of two rational numbers is always rational. This is because rational numbers can be expressed as the quotient of two integers, and multiplying two quotients of integers (fractions) results in another quotient of integers, thus another rational number.
For example, if we consider a repeating decimal like -1.2222... as -1 2/9 and √ 9 as 3, their product is -1 2/9 * 3, which simplifies to a rational number, -4 2/3, proving the result is rational.