Squares Can Be Computed Squentially

In case A is a successor of a number with a known square, you find A⊃ by adding to the latter itself and then A. For example, A = 111 is a successor of a = 110 whose square is 12100. Added to this 110 and then 111 to get A²:

111²= 110² + 110 + 111
 = 12100 + 221
 = 12321.

Why does this work?

If A = a + 1, then A² = (a + 1)² = a² + a + (a + 1).

Another example. Let A = 46. Then a = 45. It's easy to find 45² = 2025. It then follows that 46² = 2025 + 45 + 46 = 2116.


Related material
Read more...

  • Multiplication by 9, 99, 999, (Multiply + Subtract) etc.
  • Squaring 2-Digit Numbers
  • Division by 5
  • Multiplication by 2
  • Multiplication by 5
  • Multiplication by 9, 99, 999, etc. (Something Special)
  • Product of 10a + b and 10a + c where b + c = 10
  • Product of numbers close to 100
  • Product of two one-digit numbers greater than 5
  • Product of 2-digit numbers
  • Squaring Numbers in Range 26-50
  • Squaring Numbers in Range 51-100
  • Squares of Numbers That End in 5
  • How to Compute Fast Any Square
  • Adding a Long List of Numbers
  • |Contact| |Front page| |Contents| |Algebra| |Math magic| |Store|

     

    Copyright © 1996-2017 Alexander Bogomolny

     61186689

    Search by google: