Final answer:
The square root of 110 falls between the two whole numbers 10 and 11. These two numbers are square roots of 100 and 121, respectively, which are the perfect squares closest to 110.
Step-by-step explanation:
The student is asking which two whole numbers the square root of 110 falls between. To find these numbers, we want to identify the two consecutive whole numbers whose squares are immediately below and above 110. We can estimate that the square root of 100 is 10, and the square root of 121 is 11, so the square root of 110 falls between 10 and 11.
It is important to remember that whenever an equation contains an unknown squared, there are typically two solutions, but in the context of real numbers and square roots, we consider only the non-negative root. In applied contexts, like figuring out the time it takes to utilize a freeway on-ramp, only one solution typically makes sense.
When taking square roots of exponentials, you might need to adjust exponents to make the base more manageable before taking the root. For example, 5¹ (∙ 5¹) is 5², and we can interpret 5 as the square root of 5 because 5 (∙ 5) equals 5.