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Simpler way to find squares by hand?


Best Answer witzar, 31 March 2013 - 09:39 PM

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#1 BMAD

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Posted 31 March 2013 - 08:41 PM

You could take any number and square it on a calculator and find its value.  If you do not have means to find the square with technology it is still generally simple to manually compute such a square.  However, there are some instances when such a square may be challenging.  When this situation arises, there is a simple and straightforward approach:

 

let x be the number you wish to square then

 

x - 25 = the hundreds value

 

(50 - x)^2 = the ones value

 

add them together and you have your square.  It is that simple.
 

Examples:

 

46^2 = 

 

46-25 = 21 [hundreds] AND  (50-46)^2= 4^2=16, so 46^2 = 2116

 

43^2=

 

43-25 = 18  AND (50-43)^2 = 7^2=49, so 43^2 = 1849

 

and just to show you a silly example as further evidence that it works...

 

4^2 =

 

4-25= -21 AND (50-4)^2= 46^2 = 2116  and -2100 + 2116 = 16 !!  so 4^2=16

 

Now your task is to either prove this true for all real numbers or find 1 counter example.  If a counter example is found, then for what numbers is this true?

 

 

 

 

 


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#2 witzar

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Posted 31 March 2013 - 09:39 PM   Best Answer

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