)r Tr+1 would free from radical sign if powers of y and x are integers. i.e.
55−r
5
and
r
10
are integer. ⇒r is multiple of 10 . Hence, r=0,10,20,30,40,50 It is an A.P. Thus, 50=0+(k−1)10 50=10k−10⇒k=6 Thus, the six terms of the given expansion in which x and y are free from radical signs.