Proving that Any Number Ending in 5 Squared Equals 25

[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?

 

[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.

 

[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?

 

[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

 

[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

 

[matt grime]

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

 

[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.

 

[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?

 

[himanshu121]

Ya this is the property which is applied in vedic maths

 

[HallsofIvy]

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