Final answer:
The square root of 13 falls between 3 and 4.
Step-by-step explanation:
To determine which two positive integers each square root falls between, we can use the number line. In this case, the square root of 13 falls between 3 and 4 (option A). This can be seen by locating the square root of 13 on the number line and noting that it falls closer to 3 than to 4. Therefore, option A) √13 falls between 3 and 4 is the correct answer.