Final answer:
The square root of 75 falls between the perfect squares of 64 (8²) and 81 (9²), as 64 is the largest perfect square less than 75, and 81 is the smallest perfect square greater than 75.
Step-by-step explanation:
The student is asking which two perfect squares the square root of 75 falls between. To answer this, we need to find the perfect squares close to 75 that form an interval wherein √75 is located.
Firstly, we identify that the square root of 64 is 8 and the square root of 81 is 9. Since 64 < 75 < 81, the two perfect squares that √75 falls in between are 64 (8²) and 81 (9²).
Therefore, √75 is greater than 8 but less than 9, meaning it lies between the squares of the integers 8 and 9. In other words, the perfect squares between which √75 lands are 64 and 81.