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Mental Maths Workbook - squaring a number trick

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Squaring a number is simple - once you know the trick!

Let us say you want to find the square of 16.


The trick is as follows Multiply the two numbers and then add the

  1. Add or subtract a single digit number to the multiplier so that it becomes a multiple of 10.
  2. Add the same number to the multiplicand.
  3. Compute the product of the numbers from the first two steps. This multiplication is simple because it is effectively a single digit multiplication with a zero appended to the result.
  4. Add the square of the number used in step 1 and 2 to the result of step 3.

The above is illustrated in the below figure.


Note that we have to add the square of the number used to round to 10 (4 in the example above). We normally want to keep this number as low as possible. For instance, we could have used 6 in the above instance to round to 10. However, it would have ment that we would have to add 36 in the last step. This would be more difficult than adding 16. So, if we were calculating squares of numbers where the units digit was a low number, then we would round down to the lower multiple, as in the below example:


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