Can someone please please help me with the following question(s). I have been trying for hours and have got nowhere
Let p1, p2, p3, be distinct primes.
1) prove by induction on m that if x є Q and √x є Q(√p1 ..√pm ) then
x = p1^α1 ..pm^αm y^2 for some integers a1....am and some y є Q.
2) Deduce that for any n √p n+1 (n+1 subscript) is not an element of
Q(√p1 ..√pn )
3) hence prove by induction on n that [Q(√p1 ..√pn ):Q] = 2^n