HP50g simplifing a root

[Albert Chan]

Here is an equivalent version, faster and shorter.

sign(b√k) = sign(b) = sign(m)

\(|b| \sqrt{k} = |b| \sqrt{{n/a-a^2 \over 3b^2}}
= \sqrt{{n/a-a^2 \over 3}} \)

XCas> find_a(n,m) := remove(a -> remain(3*m, n/a+8*a*a), divisors(n) .* sign(n))
XCas> find_ar(n,m) := map(a -> a + sign(m)*sqrt((n/a-a*a)/3) , find_a(n,m))

XCas> find_ar(300940299, 103940300)      → \([99 + 100 \sqrt{101}]\)