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

 Nov 30, 2021
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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.

 

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

So let's look at the 28th 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.  

.

 Nov 30, 2021

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