Find the square of a number (nearing to 100) in head

How much is 5 ² ? How about 12 ² ? Well, if you have already finished the gymnasium then maybe you are already used to find the square for these numbers. But how about 104 ² ? I found another useful technique which helps you  square any number in head (no need for pen and paper). Let's take 104 ² for example:

• add to our number the last digit(s) which are above 100 (I mean 104-100 = 4) : 4 + 104 = 108; so the first digits of our square are 108

• next find the square of the last digit(s) which are above 100 of that number: 4 ² = 16

So the answer is: 104 ² = 10816. Let's try 112 ²:

• note that we are working in base 100, because 112 is an x + 100.

• add to our number the last digits which are above 100 (I mean 112 - 100 = 12) : 12 + 112 = 124; so the first digits of our square are 124

• next find the square of the last digit(s) which are above 100 of that number: 12 ²=144

So the answer is: 112 ² = 12544. Note that the 1 and the 4 above should be sum up (which is 5) because we can add to the end just 2 digits (our base 100 has only 2 zeros). If the number we try to square is below the base (below 100) we use little bit the same technique with some minor differences. Let's have 96 ² for example:

• because 96 is below our base 100, we find how much our number needs to make 100; 96 - 100 = -4

• add that difference to our number: 96 -4 = 92, so we get the first two digits of our square

• next find the square of that number which is over/under base (in our case under base); this is -4 ² = 16; so the last two digits of our square is 16

The answer is : 96 ² = 9216 Note: although I've said it helps you to square any number in head I must emphasis that it is very important to choose the number to square in head nearest 100, otherwise this method is not efficient.