Answer: 3 and 4 is what your teacher is probably looking for, but there are technically infinite solutions to the first question.
3 is a better estimate for the square root of 12 since 3 times 3 = 9 which is 3 integers away from 12, where as 4 times 4 = 16, which is 4 integers away from 12.
Explanation:
Calculate the square root of 12 which is roughly 3.464
Whole numbers are non-fractional. They can be any positive integer, as well as zero.
3.464 is between 3 and 4.
3 is less than 3.464 which is less than 4.
3 < 3.464 < 4
Technically there are infinite solutions to this problem, since 3.464 is also between 3 and 4, 3 and 5, 3 and 6, 2 and 4, 2 and 5, and infinitely more.
Question 2:
3*3 = 9.
4*4 = 16.
12-9 = 3.
16-12 = 4.
3 < 4.
12 is closer to 9 than it is to 16.