Final answer:
There are infinitely many rational numbers with square roots between 10 and 10.1, because the set of rational numbers is dense, meaning there are always more rationals to find between any two given numbers.
Step-by-step explanation:
The question at hand is determining how many rational numbers there are with square roots falling between 10 and 10.1. To find this, we must first square 10 to get 100, and then square 10.1 to get about 102.01. Recognizing that squaring a number yields another rational number if the original number was rational, we can deduce that every number between 100 and 102.01 will also have a rational square root.
Since the set of rational numbers is dense, meaning between any two rational numbers is another rational number, there are actually infinitely many rational numbers whose square roots are between 10 and 10.1. Importantly, the calculation is not about finding specific numbers but understanding the property of the density of rational numbers.