My textbook is going through an example on splitting fields. It asked to find a splitting field for x^4 - 6x^2 - 7 over the rational numbers. This polynomial factors to (x^2 - 7)*(x^2+1) which has roots of 7^(1/2) and i. So i figured the extension field E we are looking for is Q(i)(7^(1/2)), but my textbook jumps straight to Q(i)(2^(1/2). is the squareroot of 7 an element of the simple extension of the rational numbers with the square root of two? I can't imagine it being (yet i can't imagine many things that are..). Any mathamaverick wanna shed some light on my situation?