Can an irrational number be constructed which is a) not any known transcendental number b) not a surd? If yes, then how can I construct one?

fabianmartinOTQ

fabianmartinOTQ

Answered question

2022-11-27

Can an irrational number be constructed which is a) not any known transcendental number b) not a surd? If yes, then how can I construct one?

Answer & Explanation

Aileen Powers

Aileen Powers

Beginner2022-11-28Added 12 answers

Yes. If you know about Galois theory, you need an extension of Q that has a non-solvable Galois group (like S 5 ). If you don't know about Galois theory, then the roots of the polynomial x 5 80 x + 5 are irrational numbers but they are not surds and not transcendental.

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