Problem: If
N=5β+1β5β+2β+5ββ2βββ3β22ββ
then N equals
Answer Choices:
A. 1
B. 22ββ1
C. 25ββ
D. 25ββ
E. None of these
Solution:
A direct calculation shows that
(5ββ+15β+2β+5ββ2ββ)2=2
and
3β22β=2β22β+1=(2ββ1)2
Since a radical sign denotes the positive square root,
N=2ββ(2ββ1)=1.