The squares of three consecutive natural numbers add up to 110. What is the sum of the three numbers?

Explanation

1. 01

   Let them be $n - 1, n, n + 1$: the squares add to $3n^2 + 2$.

2. 02

   $3n^2 + 2 = 110$, so $n^2 = 36$ and $n = 6$.

3. 03

   The numbers are 5, 6, 7 (check: $25 + 36 + 49 = 110$); their sum is 18.