Can someone please please help me with the following question(s). I have been trying for hours and have got nowhere

Thanks

Edgar

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