somebody gave me this answer to the question in the title:
A2A: Observe that the remainder you get when you divide any square by 7 is never 3. You only need to observe it for the squares of the first 7 integers.
You also have to know that √m is rational if and only if m is a perfect square.
why does the remainder need to be 3 for it to be a perfect square?
In: 0
A number can only be a perfect square with a remainder of 3 when divided by 7 if it is both A) a perfect square and B) a number that has a remainder of 3 when divided by 7
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