Consider Q[sqrt(2)].(adsbygoogle = window.adsbygoogle || []).push({});

Does every element of Q[sqrt(2)] have a square root in Q[sqrt(2)] ?

Prove if true, and give a counterexample if false.

My solution:

sqrt(sqrt(2)) = a + bsqrt(2)

if I square both sides then I will have :

sqrt(2) = (a + b*sqrt(2))^2

= a^2 + 2ab*sqrt(2) + 2b^2

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I think the answer should be false. Am I right?

If I am right. Can you suggest me a counterexample. Thank you very much.

If I am wrong. Please correct me. Thanks

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