The sum of square roots problem

Bound how close two sums of k square roots of integers up to n can be, and decide whether such sums can be compared in polynomial time.

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File it in the catalog (shoal-catalog 0521c19bbd38)

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	1	+{
	2	+ "domain": "computer-science",
	3	+ "topics": [
	4	+ "algorithms-complexity",
	5	+ "computational-geometry",
	6	+ "number-theory"
	7	+ ],
	8	+ "type": "proof",
	9	+ "also": [
	10	+ "algorithm"
	11	+ ],
	12	+ "source": {
	13	+ "key": "topp",
	14	+ "name": "The Open Problems Project",
	15	+ "url": "https://topp.openproblem.net/p33",
	16	+ "id": "33",
	17	+ "curator": "Erik D. Demaine, Joseph S. B. Mitchell and Joseph O'Rourke",
	18	+ "poser": "Joseph O'Rourke",
	19	+ "status": "open",
	20	+ "as_of": "2026-10-20",
	21	+ "catalog": "0521c19bbd38"
	22	+ }
	23	+}