Proving that Any Number Ending in 5 Squared Equals 25

  • Context: High School 
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Discussion Overview

The discussion revolves around the mathematical property of squaring numbers that end in 5, specifically whether any number ending in 5, when squared, results in a number that ends in 25. Participants explore various approaches to prove or clarify this property, including algebraic expansions and examples.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses confusion about proving that any number ending in 5 squared equals 25, suggesting an algebraic approach but feeling it may be redundant.
  • Another participant interprets the question differently, suggesting it may relate to divisibility by 25 rather than a direct statement about squaring numbers ending in 5.
  • Several examples are provided to illustrate that numbers like 5, 15, and 25 squared end in 25, but the participant questions how to formally prove this property.
  • Another participant proposes that numbers ending in 5 can be expressed in the form of 10r + 5, indicating that this representation could be useful for further exploration.
  • There is a request for further elaboration on the algebraic expansion of (10r + 5)² to demonstrate that the last two digits must be 25.
  • A participant comments on the assumption that the original poster has basic algebra skills, suggesting that the question may stem from a homework context.
  • One participant mentions a connection to Vedic mathematics, implying that this property is recognized in that context.
  • A later reply indicates that sarcasm was used in response to a previous comment, highlighting the informal tone of the discussion.

Areas of Agreement / Disagreement

Participants express differing interpretations of the original question, with some focusing on the property of squaring numbers ending in 5, while others consider the implications of divisibility. The discussion remains unresolved as participants explore various viewpoints and approaches.

Contextual Notes

Some participants express uncertainty about the algebraic skills of the original poster, and there is a lack of consensus on the best method to prove the property in question. The discussion includes assumptions about the mathematical background of participants.

ruud
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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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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?
 
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
 
square 10r+5 you get a 25 and something that is a multiple of 100.
 
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.
 
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
 
  • #10
Actually, Matt, I was being sarcastic. You had given very good answers and the orginally poster repeatedly asked for more.
 

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