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 Why can't square numbers end in 2,3,7, or 8?
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JessColleen
New Member

United Kingdom
2 Posts

Posted - 08/10/2014 :  13:22:28  Show Profile  Reply with Quote
Need a proof for this! Cannot find one anywhere so hoping some knows it. Also, am I right in saying that quartic numbers (x^4) cannot end in 2,3,4,7,8 or 9. If so can anyone show me a proof for that? If not can anyone show me a proof for what they can end in? Thank you!
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TchrWill
Advanced Member

USA
80 Posts

Posted - 08/11/2014 :  10:44:07  Show Profile  Reply with Quote
quote:
Originally posted by JessColleen

Need a proof for this! Cannot find one anywhere so hoping some knows it. Also, am I right in saying that quartic numbers (x^4) cannot end in 2,3,4,7,8 or 9. If so can anyone show me a proof for that? If not can anyone show me a proof for what they can end in? Thank you!



SQUARES

* A square, sometimes called a perfect square, is the result of multiplying a number by itself as in N = nxn = n^2.

* The perfect squares are the squares of the counting numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, etc. which produce 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, etc.

* The last digit in the square of a number must be one of the following: 0, 1, 4, 5, 6, or 9. Note that there are numbers that end in these digits that are not squares but to be a square, they must end in one of these digits.

* If the last digit of a number is 0, its square ends in 00 and the preceding digits form a square.

* If the last digit of a number is 1 or 9, its square ends in 1 and the number formed by the preceding digits must be divisible by 4.

* If the last digit of a number is 2 or 8, its square ends in 4 and the preceding digit must be even.

* If the last digit of a nuber is 3 or 7, its square ends in 9 and the number formed by the preceding digits must be divisible by 4.

* If the last digit of a number is 4 or 6, its square ends in 6 and the preceding digit must be odd.

* If the last digit of a number is 5, its square ends in 25 and the preceding digits must be 0, 2, 06 or 56.

* The last two digits of a 3 or more digit square number must be one of the following: 00, 01, 04, 09, 16, 21, 24,
25, 29, 36, 41, 44, 49, 56, 61, 64, 69, 76, 81, 84, 89, or 96.

* The sum of the digits in a square MUST add up to 1, 4, 7, or 9.




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