set M = { a where a is Element of R : ex n being Element of NAT st a |^ n in I } ;
not { a where a is Element of R : ex n being Element of NAT st a |^ n in I } is empty

proof

consider a being Element of I;
a |^ 1 = a by BINOM:8;
then a in { a where a is Element of R : ex n being Element of NAT st a |^ n in I } ;
hence not { a where a is Element of R : ex n being Element of NAT st a |^ n in I } is empty ; :: thesis: verum

end;

hence not sqrt I is empty ; :: thesis: verum