Can you get any irrational number using square roots?

hawwend8u

hawwend8u

Answered question

2022-05-28

Can you get any irrational number using square roots?

Answer & Explanation

Campasenabs

Campasenabs

Beginner2022-05-29Added 7 answers

The smallest set of numbers closed under the ordinary arithmetic operations and square roots is the set of constructible numbers. The number 2 3 is not constructible, and this was one of the famous greek problems: the duplication of the cube.

If you allow roots of all orders, then you're talking about equations that can be solved by radicals. Galois theory explains which equations can be solved in this way. In particular, x 5 x + 1 = 0 cannot. But it clearly has a real root.

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