Squaring Any Three-Digit Number Ending IN 25

The square of 25 is 625. Oddly enough, these are the last three digits in the square of any three-digit number ending in 25. Since squaring a three-digit number results in at most six digits, the problem here is merely to find the first three digits of the answer.

Rule:   The First two digits (that is, the hundred-thousands digit and the ten- thousands digit) are found by squaring the hundreds digit of the given number and adding to the result one-half the hundreds digit of the given number (ignoring the fraction 1/2 if it occurs). If the result is a one-digit number, then there is no hundred-thousands digit in the answer and the result is the ten-thousands digit of the answer. The thousands digit of the answer is 5 if the hundreds digit of the given number is odd and 0 if the hundreds digit of the given number is even, Affix 625 to obtain the final answer.

Two illustrative examples will be used to demonstrate the ease with which this short cut may be used. 

Example:

Square 225.

First, square the hundreds digit of the given number, to obtain

           4

To this add one-half the hundreds digit of the given number.

           4 + 1 = 5

Since the answer is a one-digit number, 5 is the ten-thousands digit of the answer. The thousands digit of the answer will be 0, since the hundreds digit of the given number, 2, is even. To this we affix 625 to obtain the final answer.

         50,625 Answer