Final answer:
The correct simplification of √9a³ is 3a√a, as you apply the square root to both the numerical and variable parts of the expression separately.
Step-by-step explanation:
The student is asking about simplifying a square root expression involving a variable with an exponent. The expression given is √9a³. To simplify, recall that the square root of a square is just the base of the square. For instance, √9 is simply 3 because 3² equals 9. Similarly, √a³ involves taking the square root of a cubed variable, which results in one factor of the variable left under the square root sign, since a³ is a² times a.
Using this principle, we take the square root of 9a³ to get 3a√a, because √9 equals 3, and √a³ gives us a² (which is a) times a (under the square root). So the correct answer to take the factor out of the square root of 9a³ is 3a√a.