Simple Method for Calculating Shortcut for Square - Part 2

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We've already seen how to find the squares of numbers which are one more than those whose squares we already know (eg 25, 30, 35 etc).Read that post Here. Similarly, we can find the squares of numbers which are one less than the numbers whose squares are known already to us. For Example,

292 = 30 - 30th odd number = 900 - 59 = 841

392 = 40 - 40th odd number = 1600 - 79 = 1521

342 = 1225 - 69 = 1156

542 = 3025 - 109 = 2916

742 = 5625 - 149 = 5476

942 = 9025 - 189 = 8836

2142 = 46225 - 429 = 45796

So, we have seen how to get the squares of numbers which are one more or one less than the numbers whose squares we already know (i.e., 25, 30, 35, 40, etc)

Now, we shall see how to get the squares of numbers which are 2 more or less than the numbers whose squares we already know.

272 = 262 +  27th odd number = 252 + 26th odd number + 27th Odd number.

The sum of the 26th odd number and 27th odd number is the same as 4 times 26

So, 

272  = 252 + 4x26 = 625 + 104 = 729

572  = 3025 + 224 (4 times 56) = 3249

77 2 = 5625 + 304 (4 times 76) = 5929

972  = 9025 + 384 (4 times 96) = 9409

Similarly,  we can find out the squares of numbers which are 2 less than the numbers whose squares we know

282 = ( 302  - 4 times 29) = 900 - 116 = 784

532  = (552 - 4 times 54) = 3025 - 216 = 2809

932  = 9025 - 376 = 8649

2432 = 60025 - 976 = 59049

Note : You should do all these calculations MENTALLY. I mean without using pen or pencil. So practice well to do these problems orally. 

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