## Simple proof

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?
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 Recognitions: Homework Help Science Advisor 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.
 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?

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Homework Help

## Simple proof

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
 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
 Recognitions: Homework Help Science Advisor square 10r+5 you get a 25 and something that is a multiple of 100.
 Recognitions: Gold Member Science Advisor Staff Emeritus 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.
 Recognitions: Homework Help Science Advisor 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?
 Ya this is the property which is applied in vedic maths
 Recognitions: Gold Member Science Advisor Staff Emeritus Actually, Matt, I was being sarcastic. You had given very good answers and the orginally poster repeatedly asked for more.

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