*aren't*the square of an integer, but it's going to be a lot easier and faster to count how many

*are*the square of an integer*:

1

^{2}= 1

2

^{2}= 4

3

^{2}= 9

4

^{2}= 16

5

^{2}= 25

6

^{2}= 36

7

^{2}= 49

8

^{2}= 64

9

^{2}= 81

10

^{2}= 100 ...and we're done! (Any higher will be out of the range we care about.)

Count how many we've got. I'm counting 10.

There are 100 integers between 1 and 100 inclusive (inclusive just means "including the ends," so we are counting both 1 and 100), and only 10 of them are squares of integers. Which means 90 aren't. The answer is (E).

* This is kinda like a shaded region area problem in that way...it's easier to look for the opposite of what they ask for, and then subtract.