help math

 

The positive difference between two consecutive even perfect squares is 228. Compute the larger of the two squares.  

 

Let's make a list and check it twice, to see if we can discern a pattern.  

 

Even Square    Next Even Square    Difference   

 

           4                           16                    12  

         16                           36                    20  

         36                           64                    28  

         64                         100                    36  

       100                         144                    44  

       144                         196                    52  

       196                         256                    60  

       256                         324                    68  

 

What I see is that the difference between the squares increases by 8 every time.  

 

Let's divide 8 into 228 and see if that gives us a plausible starting point.  228/8 = 28.5 

 

We've been taking the square of every even number, that is, 2,4,6,8, etc. 

So let's look at the 28^th even number, that is, 56.  We'll try 56² and 58² and see what happens.  

 

56² is 3136 and 58² is 3364.  What does 3364 – 3136 equal?  3364 – 3136 = 228  

 

Hot dang, got it the first try.  I really expected to have to try at least twice.  Oh well.  

 

So, "Compute the larger of the two squares" is 3364 and there's your answer.  

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