Prove: Every Int Ending in 5 to Square End in 25

[Hollysmoke]

I don't get any of this and the textbook doesn't help that much either. I was wondering if someone could help me wiht this one question:

Prove that every positive integer, ending in 5 creates a number that when squared, ends in 25.

 

[matt grime]

What did you try? As a hint, what happens if I square 10x for an x?

 

[Hollysmoke]

I didn't try anything because I just don't understand. But I think we have to make it so that a number ending in 5, so 5,15,25, that when squared = ****25

 

[HallsofIvy]

Please don't double post! I'll add what I did to matt grime's post in the other thread. Any integer, ending in 5, can be written in the form 10x+ 5 where x is an integer. What is (10x+ 5)²?

 

[Hollysmoke]

I didn't double post this topic. It may have been someone else with a similar topic.

(10x+5)^2 =100x^+100x+25

And it's 10x+5=*5, which we square, right?

 

[matt grime]

But I think we have to make it so that a number ending in 5, so 5,15,25, that when squared = ****25

you do not have to 'make it' since it is true, and that is what you're tying to prove.

oh, and you're expansion is slightly off, but surely you can see the answer now, if not express exactly what you need to.

 

[Hollysmoke]

So when I am looking at these types of questions, I should presume that it is true?

 

[matt grime]

Eh? You're asked to prove it is true, so unless there is a mistake somewhere (which is very possible), the answer *is* true, but you cannot assume it is true. But in any case, that has nothing semantically to do with you statement that you want to 'make' it true. *You* do not *make* it true.

 

[Hollysmoke]

Okay I understand. I'm not MAKING it true, I'm just trying to show that it either IS or IS NOT true.

 

[HallsofIvy]

I didn't double post this topic. It may have been someone else with a similar topic.

(10x+5)^2 =100x^2+100x+25

And it's 10x+5=*5, which we square, right?

(10x+5)^2 =100x^2+100x+25= 100(x^2+ x)+ 25. What are the last two digits of 100(x^2+ x)? What does that tell you?

(Since you haven't explained what "*" means, I have no idea what you mean by 10x+ 5= *5.)