A Trick for Squaring Numbers in Your Head

Daniil Victorevich Avatar

During that long trip back from Leningrad to Moscow, Gersa gave me a two-digit number to square.

The number was 57.

57×57 sounds hard to do in your head, but there’s a trick.

First, simplify the problem by rounding:

  • Take 57 and add 3 to make 60.
  • Next, subtract 3 from 57 to make 54.

Now, you’ll need to multiply 60 and 54.

Drop the zero in 60 for now because 6 x 54 is simple:

  • 6 x 50= 300, and 6 x 4 = 24
  • Add those to get 324

Add a zero to it to get 3,240

All that’s left is to square the 3 you knocked off the equation and add it back in.

3^2=9

3,240+9=3,249

There you go.

57^2 = 3,240

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