### 5.8 Root Extraction Functions

Function: int mpz_root (mpz_t rop, const 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_rootrem (mpz_t root, mpz_t rem, const mpz_t u, unsigned long int n)

  Set root to the truncated integer part of the nth root of u. Set rem to the remainder, u-root**n.

Function: void mpz_sqrt (mpz_t rop, const 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, const 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 (const 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 (const 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.