Simple proof

1. Feb 11, 2004

ruud

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. Feb 11, 2004

matt grime

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.

3. Feb 11, 2004

ruud

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?

4. Feb 11, 2004

matt grime

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

5. Feb 11, 2004

ruud

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

6. Feb 11, 2004

matt grime

square 10r+5 you get a 25 and something that is a multiple of 100.

7. Feb 12, 2004

HallsofIvy

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.

8. Feb 12, 2004

matt grime

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?

9. Feb 12, 2004

himanshu121

Ya this is the property which is applied in vedic maths

10. Feb 13, 2004

HallsofIvy

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