+660 For how many positive integers N does √N differ from 10 by less than two?
+9481 The difference between √N and 10 is less than 2. So the following two inequalities must both be true:
√N - 10 < 2 and 10 - √N < 2
Looking at the first inequality:
√N - 10 < 2
√N < 12
N < 144 ( and N > 0 )
Looking at the second inequlaity:
10 - √N < 2
-√N < -8
√N > 8
N > 64 ( and N > 0 )
So N must be a positive integer in the interval (64, 144)
That is 79 integers.
