For example:  492 is close to 500, which is easy to multiply by. Add and subtract 8 (the difference between 500 and 492) to get  Multiply these numbers together to get 242,000 (This can be done efficiently by dividing 484 by 2 = 242 and multiplying by 1000). Finally, add the difference (8) squared (82 = 64) to the result:  The proof follows:  This method requires memorization of the squares of the one-digit numbers 1 to 9. The square of "mn", "mn" being a two-digit integer, can be calculated as  Meaning the square of "mn" can be found by adding "n" to "mn", multiplied by "m", adding 0 to the end and finally adding the square of "n". For example, 232:  So 232 = 529. Suppose one needs to square a number "n" near 50. The number may be expressed as "n" = 50 − "a" so its square is (50−"a")2 = 502 − 100"a" + "a"2. One knows that 502 is 2500. So one subtracts 100"a" from 2500, and then add "a"2. Example, say one wants to square 48, which is 50 − 2. One subtracts 200 from 2500 and add 4, and get "n"2 = 2304. For numbers larger than 50 ("n" = 50 + "a"), add 100×"a" instead of subtracting it. This method requires the memorization of squares from 1 to 24. The square of "n" (most easily calculated when "n" is between 26 and 74 inclusive) is  In other words, the square of a number is the square of its difference from fifty added to one hundred times the difference of the number and twenty five. For example, to square 62:  This method requires the memorization of squares from 1 to "a" where "a" is the absolute difference between "n" and 100. For example, students who have memorized their squares from 1 to 24 can apply this method to any integer from 76 to 124. The square of "n" (i.e., 100 ± "a") is  In other words, the square of a number is the square of its difference from 100 added to the product of one hundred and the difference of one hundred and the product of two and the difference of one hundred and the number.