properties of numbes - is n an integer?

[heffsz]

Can anyone explain the below? I've read the OG explanation (#146) but still don't understand how (1) is false but (2) is true. I thought the answer was D and not B. Could anyone give me an example where a non integer thats squared results in an integer?

Is n an integer?
(1) n^2 is an integer
(2) Square root of n is an integer.

Thanks!

[gkammaje]

two most simple examples are-
(1.4)^2 = 2
(1.7)^2 = 3

hope this helps

[austin]

n^2 is an integer
n^2 = 64 -> n = 8, an integer
n^2 = 63 -> n - 7.9, not an integer
INCONSISTENT ANSWERS

Square root of n is an integer.
n^1/2 = 64 -> n = 64*64, an integer
n^1/2 = 63 -> n = 63*63, an integer
ALWAYS TRUE B

[heffsz]

thanks for the responses gkammaje and austin. i originally thought about 1.4 and 1.7 but when you square either of these numbers it doesnt come out to be exactly 2 or 3. same goes for 7.9 and 63. isn't this a bit of a problem?

again, thanks for the help.