(In reply to
another form of the answer by Larry)
Repeatedly squaring and taking care of the 5's gives
x = (5((5(x²5)²)²5)²)²  5
Putting (1858)^1/8 into the RHS gives 2.562304215 (which differs in the seventh decimal place.) Raising this to the eighth power gives 1857.999223
My guess based on simpler equations like √(5√(5+x)) = x
is that the squared out form will be a degree 32 polynomial with 31 real but extraneous roots. The root that works will likely involve a 32nd root but not as simply as n^(1/32)

Posted by Jer
on 20121218 13:59:18 