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Integer Squares


The square of a number is one of the integers of the series 1, 4, 9, 16, 25, etc. It is not difficult to verify the relationship between consecutive members of this series. We find that if we add the square of x, twice more x plus 1, the next successive square is obtained.

For example , 52 + 2.5 + 1 = 25+10+ 1 = 36 = 62

If we know the value of a given number squared, the next number is easily obtained.
Example: Knowing that the square of 18 is 324, we have:

192 = 182 + 2.18 + 1 = 324+36+ 1 = 361

The reason for this fact is verified by the algebraic relation:

(a + b)2 = a2 + 2ab + b2

19 = (18 + 1) = 182 + 2.18.1 + 12 = 361