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Math Help - Square integer

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    Super Member dhiab's Avatar
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    Square integer

    If n consists of a total of five digits equal to 29, can be n square integer.
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    Quote Originally Posted by dhiab View Post
    If n consists of a total of five digits equal to 29, can be n square integer.
    Does this mean that the sum of it's digits equals 29?
    i.e if the number was 28,469 then 2+8+4+6+9=29

    If this is the case then the answer must be no, as the digital root of n is 2, where the digital root is defined as the number obtained by adding all the digits, then adding the digits of that number, and then continuing until a single-digit number is reached.

    For example: suppose x=3,298. So we sum it's digits to get 3+2+9+8=22. We then sum the digits of 22 and arrive at 2+2=4. Therefore we say that the digital root of x is 4.

    Now, a perfect square can only have a digital root of 1,4,7 or 9, thus ruling out the n given in the question. Can you see why the digital root of a square number can only equal these values?
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