S 01. Let a be an element such that a? E Q, but a € Q. (1) Show that Q(a, V2) = Q(a + V2). (ii) Show that Q (21/3,i) = Q

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S 01 Let A Be An Element Such That A E Q But A Q 1 Show That Q A V2 Q A V2 Ii Show That Q 21 3 I Q 1 (25.04 KiB) Viewed 19 times

S 01. Let a be an element such that a? E Q, but a € Q. (1) Show that Q(a, V2) = Q(a + V2). (ii) Show that Q (21/3,i) = Q(B), where ß = 24/3 i and i? = -1. = (iii) How many elements are there in the basis of Q(B) over Q? Write down the basis. (iv) Draw a lattice diagram for the fields Q. Q(a), ((v2), 2(a + v2), Q(K), Q(a,b), and Q(a,b,v2).