Friday, June 29, 2012

Square Numbers - II

Properties of Square Numbers
  • A number that ends in 2 , 3 , 7 or 8 is never a perfect square. 
  • The ones digit in the square of a number can be determined if the ones digit of the number is known. Look at the following table
                                 
  • The number of zeroes at the end of a perfect square is always even e.g.                402 = 1600 , 2002 = 40000
  • The square of an even number is always an even number and square of an odd number is always an odd number. e.g. 122 = 144 , 232 = 529
  • If n is a perfect square then 2n can never be a perfect square. e.g. 100 is a perfect square , but 2 x 100 = 200 is not a perfect square number. 
  • The difference between the squares of the two consecutive numbers is equal to their sum or twice the smaller number plus 1. e.g. 
                     (m+1) 2 - m2 = [(m+1) + m] [(m+1) – m] = (2m +1)
  • If a number is a square number , it has to be the sum of successive odd numbers starting from 1. e.g. 
               1 + 3 = 4 = 22                          [Sum of first two odd numbers]   
               1 + 3 + 5 + 7 + 9 = 25 = 52       [ Sum of first five odd numbers]

  • The square of a number , either negative or positive is always positive.          e.g. (-3) 2 = (-3) x (-3) = 9 
  • The square of a natural number other than 1 is either a multiple of 3 or exceed the multiple of 3 by 1. Thus we can express square of a number (other than 1) as 3m or 3m+1 for some natural number m. e.g.
                      52 = 25 = 3 x 8 + 1 
                    122 = 144 = 2 x 36 
  • The square of a natural number other than 1 is either a multiple of 4 or exceed the multiple of 4 by 1. Thus we can express square of a number (other than 1) as 4m or 4m+1 for some natural number m. e.g.
                    72 = 49 = 4 x 12 + 1 
                 142 = 196 = 4 x 49

4 comments:

  1. Good Post and as a Math lover I must say I enjoy your Blog :)

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  2. Some of these can be extended to broader statements. Like 2n is never a prime when n is a prime. Well, mn is a prime iff m and n are primes, right, so 2n is just a special case of this.

    Thanks for the thought provoking list!

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  3. nice post,..
    i want to share something for u about square number

    http://www.math-worksheets.co.uk/using-a-number-square-in-year-2/

    ReplyDelete