Root extraction is the operation of taking an nth root of a number.
A mental method recovers a two-digit positive integer 
from its fifth power 
(Numberphile 2014). In decimal
notation, the final decimal digit of 
equals that of 
because 
. This congruence
follows from Fermat's little theorem modulo
5 together with the fact that 
and 
have the same parity. To recover
the tens digit 
, compare 
with the fifth powers of 10, 20,
..., 100 and choose the unique 
, 2, ..., 9 for which 
. The positive fifth root is then
 |
where 
is the least nonnegative remainder when 
is divided by 10.
