Question 1024030
{{{27^(1/5)}}}

={{{(32-5)^(1/5) = 32^(1/5)+ (1/5)(32)^(1/5-1)(-5)^1 + (((1/5)(1/5-1))/(2*1))(32)^(1/5-2)(-5)^2 + (((1/5)(1/5-1)(1/5-2))/(3*2*1))(32)^(1/5-3)(-5)^3}}} +....

We stop at the first four terms of this binomial series for an estimate and compute...

= {{{2 - 1/16 - 1/256 - 3/8192}}}

= 1.933227539

=1.933, to four significant figures.