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> How can I prove that the unit digit of a perfect square is always $0,1,4,9,5,6$ and never $2,3,7,8$? 
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It's pretty intuitive but I am having difficulties proving this statement. 
 I had used trial and error to get to that statement. 

**Note**(The original problem was: If the length and width of a rectangle are consecutive positive integers and the area has $6$ in its unit digit.Is it possible to say that one of the length or width is a perfect square number ?)