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Math Help - Square number

  1. #1
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    Square number

    is equal square number ,what is the number?
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  2. #2
    Member Sylvia104's Avatar
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    Re: Square number

    Let n=123456. Then the expression is (n+1)+n+n^2=1+2n+n^2. Now factorize 1+2n+n^2.
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  3. #3
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    Re: Square number

    (n+1)(n+1)?
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  4. #4
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    Re: Square number

    Hello, Mhmh96

    You may have missed the point of Sylvia's hint . . .


    123457 \;+\; 123456 \;+\; (123456)^2\text{ is the square of an integer.}\;\text{ What is the integer?}

    Look at what we have:

    (123456)^2 + 123456 + 123457

    . . =\;(123456)^2 + 123456 + 123456 + 1

    . . =\;(123456)^2 + 2(123456) + 1

    . . =\;(123456 + 1)^2

    . . =\;(123457)^2


    \text{Answer: }\:123457

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  5. #5
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    Re: Square number

    thanks for your help,and for correcting the question.
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  6. #6
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    Re: Square number

    Now i understand what is the hint
    Last edited by Mhmh96; April 9th 2012 at 08:01 AM.
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