square root of 9 belongs to the family of 10 real numbers.
square root of 9 belongs to what family of real numbers?
10
the square root of "x" is rational if and only if "x" is a rational number that can be represented as a ratio of two perfect squares. (see square root of 2 for proofs that this is an irrational number, and quadratic irrational for a proof for all non-square natural numbers.) the square root function maps rational numbers into algebraic numbers (a superset of the rational numbers).





























for all real numbers "x",





























for all nonnegative real numbers "x" and "y",





























and
square root
for formula_25 the square root is real and the cubic root is thus well defined, providing the unique real root. on the other hand, for formula_26 the square root is not real, and one has to choose, for the square root, either non-real square root. thus the cubic root has to be chosen among three non-real numbers. if the same choices are done in the two terms of the formula, the three choices for the cubic root provide the three branches shown, in the accompanying image.
algebraic function