Final answer:
The expression 5√11 - 12√11 - 2√11 simplifies to -9√11 by combining like terms, which corresponds to option c. -9√11.
Step-by-step explanation:
The student's question involves simplifying the expression 5√11 - 12√11 - 2√11. When simplifying expressions that involve square roots, you can combine terms that have the same radical. In this case, all terms have the radical √11, so we can combine them just like like terms.
To simplify the expression, combine the coefficients of √11:
- 5√11 - 12√11 = -7√11
- -7√11 - 2√11 = -9√11
Therefore, the simplified form is -9√11. Looking at the options provided: a. -33√9, b. -11√9, c. -9√11, d. -9√33, we can see that option c is the correct answer.