Thread:Ursuul/@comment-27048378-20170119215719

Let's take the number potato, where the second and last digits are the same and the third and fifth digits are the same. Then if potato = x^2, then 317<= x <= 999. Let x = bcd, this 3-digit number.

Then bcd^2 = (100b + 10c + d)^2 = 10000b^2 + 100c^2 + d^2 + 2000bc + 200bd + 20cd

After lots of nasty calculations, you find that there are three answers:

x=543, potato = 294849

x=719, potato = 516961

x=918, potato = 842724

Of these, only x=719, potato = 516961 has common digits (o=1, a=9). So x = 7oa. The only three letter word that matches this pattern is BOA.

So the square root of potato is a boa constrictor. 