> Essentially, it means the number cannot be constructed using a finite combination of integers and standard algebraic operations (addition, subtraction, multiplication, division, and integer roots)

Slight clarification, but standard operations are not sufficient to construct all algebraic numbers. Once you get to 5th degree polynomials, there is no guarantee that their roots can be found through standard operations.

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hidroto 2 hours ago | parent [-]

I am no mathematician, but i think you may be overstating Galois result. it says that you cant write a single closed form expression for the roots of any quintic using only (+,-,*,/,nth roots). This does not necessarily stop you from expressing each root individually with the standard algebraic operations.

	▲	gizmo686 an hour ago \| parent [-]
		I think you are thinking of the Abel–Ruffini impossibility theorum, which states that there is no general solution to polynomials of degree 5 or greater using only standard operations and radicals. Galois went a step further and proved that there existed polynomials whose specific roots could not be so expressed. His proof also provided a relatively straightforward way to determine if a given polynomial qualified.