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

Guest Nov 30, 2021

#1**0 **

*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 56^{2} and 58^{2} and see what happens.

56^{2} is 3136 and 58^{2} 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.

**.**

Guest Nov 30, 2021