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(gmp.info)Integer Roots

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Root Extraction Functions
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 - Function: int mpz_root (mpz_t ROP, mpz_t OP, unsigned long int N)
     Set ROP to  the truncated integer part of the Nth root of OP.
     Return non-zero if the computation was exact, i.e., if OP is ROP
     to the Nth power.

 - Function: void mpz_sqrt (mpz_t ROP, mpz_t OP)
     Set ROP to  the truncated integer part of the square root of OP.

 - Function: void mpz_sqrtrem (mpz_t ROP1, mpz_t ROP2, mpz_t OP)
     Set ROP1 to the truncated integer part of the square root of OP,
     like `mpz_sqrt'.  Set ROP2 to the remainder OP-ROP1*ROP1, which
     will be zero if OP is a perfect square.

     If ROP1 and ROP2 are the same variable, the results are undefined.

 - Function: int mpz_perfect_power_p (mpz_t OP)
     Return non-zero if OP is a perfect power, i.e., if there exist
     integers A and B, with B>1, such that OP equals A raised to the
     power B.

     Under this definition both 0 and 1 are considered to be perfect
     powers.  Negative values of OP are accepted, but of course can
     only be odd perfect powers.

 - Function: int mpz_perfect_square_p (mpz_t OP)
     Return non-zero if OP is a perfect square, i.e., if the square
     root of OP is an integer.  Under this definition both 0 and 1 are
     considered to be perfect squares.