# 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. • 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
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