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Simple proof

  1. Feb 11, 2004 #1
    This should be an easy question but I'm having problems with it. Prove that any number that ends in five when squared equals 25. So if n is the number then

    (n/5)^2 = (n^2)/25
    Although if you expand the left side then this statement is redudant. Can someone help me with this?
     
  2. jcsd
  3. Feb 11, 2004 #2

    matt grime

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    I think you ought to reread the question - 15*15 ends in a five, do you mean if x is divisibly by 5, then x^2 is divisible by 25?

    well, 5|x implies x=5y some y, so x^2=25y^2, so 25 divides x^2 is a formal statement of it.
     
  4. Feb 11, 2004 #3
    any positive number that ends in 5 when squared ends in 25

    eg
    5^2 = 25
    15^2 = 225
    25^2 = 625

    Just scrap what I started with I don't think it helps at all, how could I prove this question?
     
  5. Feb 11, 2004 #4

    matt grime

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    oh, ok

    ends in 5 is the same as is equal to 10r+5 for some r

    safely we can leave the rest to you
     
  6. Feb 11, 2004 #5
    I wouldn't say safely could you please expand on that? every time a number that ends with 5 is squared the resulting term ends in 25
     
  7. Feb 11, 2004 #6

    matt grime

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    square 10r+5 you get a 25 and something that is a multiple of 100.
     
  8. Feb 12, 2004 #7

    HallsofIvy

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    matt grime was making the perhaps unwarrented assumption that a person asking such a question could do basic algebra.

    (10r+ 5)2= 100r2+ 2(10r)(5)+ 25
    = 100r2+ 100r+ 25
    = 100(r2+r)+ 25

    Because r2+r is multiplied by 100, 100(r2+r) will have last two digits 00. Adding 25 to that, the last two digits must be 25.
     
  9. Feb 12, 2004 #8

    matt grime

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    I was hoping that given the start the questioner would work on the answer some more and get the solution themselves. Don't know about you, Halls (if I can be familiar ;-)) but a lot of the queries appear to me to be from homework sheets; is it better to prompt the right answer or spoonfeed it verbatim?
     
  10. Feb 12, 2004 #9
    Ya this is the property which is applied in vedic maths
     
  11. Feb 13, 2004 #10

    HallsofIvy

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    Actually, Matt, I was being sarcastic. You had given very good answers and the orginally poster repeatedly asked for more.
     
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