### Calculating the mth root of a rational number

We use a discrete form of Newton's method to find \(\lfloor x^{1/m}\rfloor\), the integer part of the mth root of a positive integer x.

(See K.R. Matthews, *Computing m-th roots*, The College Mathematics Journal 19 (1988) 174-176.

Also see MP313 lecture notes and H. Lüneburg's book *On the Rational Normal Form of Endomorphisms* 1987, B.I. Wissenschaftsverlag, Mannheim/Wien/Zürich.)

Note that if x=a/b, a > 0, b > 0, is a positive rational, then
\(\lfloor x^{1/m}\rfloor=\lfloor\lfloor x\rfloor^{1/m}\rfloor\).

The answer is given truncated to r decimal places.

This is a BCMATH version of a BC function `mthrootr(a,b,m,r)` contained in the file gcd.

*Last modified 4th January 2014*

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