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

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In summary, the conversation discusses how to prove that every positive integer ending in 5, when squared, results in a number that ends in 25. The participants discuss different approaches and equations, ultimately showing that this statement is true.
  • #1
Hollysmoke
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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.
 
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  • #2
What did you try? As a hint, what happens if I square 10x for an x?
 
  • #3
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
 
  • #4
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?
 
  • #5
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?
 
  • #6
Hollysmoke said:
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.
 
  • #7
So when I am looking at these types of questions, I should presume that it is true?
 
  • #8
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.
 
  • #9
Okay I understand. I'm not MAKING it true, I'm just trying to show that it either IS or IS NOT true.
 
  • #10
Hollysmoke said:
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.)
 

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

How can we prove that every integer ending in 5 will square to a number ending in 25?

To prove this, we can use the mathematical concept of perfect squares, which are numbers that can be expressed as the product of two equal numbers. In this case, we can show that every integer ending in 5 can be written as the product of two equal numbers, thus proving that it will square to a number ending in 25.

Is there a formula or equation that can be used to prove this statement?

Yes, there is a formula that can be used to prove this statement. It is called the formula for perfect squares, which states that the square of any number ending in 5 can be found by multiplying the number in front of the 5 by the next consecutive number and then adding 25 at the end.

Can you provide an example to help understand this concept better?

Sure, let's take the number 25 as an example. It ends in 5 and when we square it, we get 625, which also ends in 25. This follows the formula mentioned before: (2 x 3) = 6 and then add 25 at the end, giving us 625.

Does this statement apply to all integers ending in 5, no matter how large or small?

Yes, this statement applies to all integers ending in 5, regardless of their size. This is because the formula for perfect squares is a general rule that can be applied to any integer ending in 5.

Why is it important to prove this statement?

Proving this statement is important because it helps us understand the mathematical patterns and relationships between numbers. It also allows us to make accurate predictions and solve more complex mathematical problems involving perfect squares and integers ending in 5.

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