Calculate Square Numbers

This article shows a trick how everyone can calculate square numbers easily in your head. You don't need a calculator!


Example:  232 = 529

The rule: Find the nearest tenner for 23, which is 20

               Now calculate: ((23-3) * (23+3)) + 32 =
                                        20 * 26 + 9 =
                                        520 + 9 =
                                        529

 


Example:  462 = 2116

The rule: Find the nearest tenner for 46, which is 50

Now calculate: ((46+4) * (46-4)) - 42 =

               Now calculate: ((46+4) * (46-4)) + 42 =
                                        50 * 42 + 16 =
                                        100 * 42 / 2 + 16 =
                                        2100 + 16 =
                                        2116


 General Rule for x

The rule: Find the next tenner for x, which is x+a or x-a

Now calculate: ((x+a) * (x-a)) + a2

Proof:  ((x+a) * (x-a)) + a2 =
            (x2 + x*a - a*x - a2) + a2 =
            x2 - a2 + a2 =
            x2

 

 

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