Multiplying Square Numbers from 51 to 59

Multiplying square numbers from 51 to 59 is very simple.  In fact, it can probably be done more quickly than with a calculator.  All that is needed is the rule.

The secret to multiplying square numbers from 51 to 59 is to apply three steps.  The first step is to square the first digit of the number.  With the numbers 51 to 59, the first digit is always 5 and the square is always 25.  Next we add this number to the digit on the right.  For example, if we take the number 51, the square of 5 is 25.  We add this to the 1 on the right and get 26.  Next we square the number on the right and make sure that we have two digits.  We square the number 1 and write 01 because we need two digits.  The product is 2601.

Now we can do the same with 52.  We square the number 5 and get 25.  We add this to the number 2 and get 27.  Next we square the number 4 and write 04.  The product is 2704.

Finally we can try this with a larger number.  Let us try 59.  We square the number 5 and get 25.  To this number we add 9 and get 34.  Now we square 9 and get 81.  The product is 3481.

Here are the squares of the numbers 51 to 59:

51x51=2601
52x52=2704
53x53=2809
54x54=2916
55x55=3025
56x56=3136
57x57=3249
58x58=3364
59x59=3481

The rule for multiplying squares from 50 to 59 has only three steps.  By applying this rule, these squares can be multiplied quickly and easily.  With knowledge of this rule, a calculator is not needed.