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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
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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square of 53 is 2809 and not 2089...kindly corect it..i think its printing mistake..
ReplyDeleteYep its a typing mistake friend. Corrected it now :)
DeleteSorry for the inconvenience..
A GENERALIZED FORMULA CAN BE DRAWEN
ReplyDeletefor no ending 6 and 1
(n-1)^2+(2n-1)
for no ending 4 and 9
(n+1)^2-(2n+1)
confused with 74²
ReplyDelete..actually to find odd number we use (2n-1), therfore 74²=75²-74th odd number
5625-(2*74-1)=5625-(148-1)
therefore answer should be 5578 which is wrong but u have taken 149...hw is that plz explain
Sorry i got that.. i should have taken 75th odd number but i made mistake by taking 74th :(
ReplyDeleteThanks :)