Final answer:
The simplified form of √45 is 3√5, which factors the number into its prime components and simplifies the square root of the perfect square 9 to 3.
Step-by-step explanation:
The simplified form of √45 is the same as simplifying the square root of a product of its prime factors. The number 45 can be factored into 9 and 5, where 9 is a perfect square (3²). Therefore, when we take the square root of 45, we can split it into the square root of 9 times the square root of 5 (√9 * √5).
Since the square root of 9 is 3, we simplify √45 to 3√5. This corresponds to option C in the proposed answers.