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Wednesday, May 30, 2012

Shortcut for Square - A Simple Method

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7e ha+e alread% discussed a method for finding the s8uares of the gi+en num-er 9check

that method Here:. No4 4e shall discuss another simplest method to calculate s8uare of the gi+ennum-er. 0irst of all one thing %ou should keep in mind, for %ou r con+inience 4e;+e mentioned each ande+er% step in detail. But You should do all these calculations MENTALLY. I mean without usingpen or pencil. So practice well to do these problems orally. Now lets go to thetopic, 0inding the s8uare of a num-er ending in / is +er% simple. If the last digit of the num-er is /, thenthe last t4o digits of the s8uare 4ill -e /.7hat e+er is the earlier part of the num-er multipl% it 4ith onemore than itself and that 4ill -e the first part of the ans4er. 92he second part of the ans4er 4ill -e /onl%:.

</ = "/ Here < ) # = " so the ans4er is "/

#/ = !/

// = <!/>/ = /5/

?/ = ?!/

"/ = "/5/

">/ = <!5/

</ = ///

"?/ = <@!/

#/ = 5!!/

7ell friends, no4 4e kno4 the s8uares of num-ers /, <!, </, #!, #/, /!, // etc. If 4e 4ant to find the

s8uares of an% other num-er, 4e find it using these s8uares 4hich 4e alread% kno4.

0or 5 4e 4ill go from /, for < 4e go from <! and so on.

'ne 4a% is 4riting 5 = 9/":. But 4e need not e+en calculate 9a-: -% adopting the follo4ing

method.

5 = /  5th odd num-er. i.e., 5/ /" = 5>5

9a-: = a a- -

5 = 9/ " :  = / ) / ) " "

  = 5/ /! "  = 5/ /"

8/9/2019 Another Simple Method for Calculating

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  = 5>5 So, the ans4er is same. No4 4e shall look at an easiest method 4hich 4ill help %ou to calculate S8uares$entall%.

" = " = "

= # = "<

< = ? = " < /

# = "5 = " < / >

/ = / = " < / > ?

I mean, to get n, %ou should add the 0IRS2 n odd num-ers. If 4e 4ant "> , it 4ill -e the sum of the

0IRS2 "> odd num-ers.

nth odd number is equal o !2n " 1#

Suppose %ou 4ant to find out 5 kno4ing 4hat / is, 4e can mo+e from / to 5.

5 4ill -e the sum of "st 5 odd num-ers. But the sum of the first 5 odd num-ers can -e 4ritten as Sumof the first / odd num-ers Si)th odd num-er. Since 4e alread% kno4 that the sum of the 0IRS2 /

odd num-ers is / , i.e., /, 4e need to add the si)th odd num-er, i mean 9) 5": = "" to / to gi+e us

5 = <5.

Similarl%<" = ?!! <"st 'dd num-er = ?!! 5" = ?5"

<5 = "/ <5th odd num-er = "/ >"

= "?5 9remem-er that </ = "/:

#" = "5!! @" = "5@"

#5 = !/ ?" = ""5"5 = "/5/ /" = "/@>5

"?5 = <@!/ <?" = <@#"5

"5 = #5/ #5" = #55/5 Read $ore ☛

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