What is the arithmetic square root? The principal value of the square root of a non-negative number. What is the principal value of the square root of a non-negative number?

The square root of C is actually the value of the solution X of X 2 = C. When C is not equal to 0, X will have two solutions. And one of these two solutions is the most important principal value. For positive real numbers, the principal value is the positive root.

So the positive solution of x 2 = c is the arithmetic square root of c, which is represented by the root sign C.

In fact, the root sign of higher order also takes the principal value. The principal value of the n-th root of a positive number is the one that takes a positive number. Even the roots of negative numbers are generally not considered in middle schools. But the odd roots of negative numbers will be considered in middle school. The principal value of the odd root of a negative number is negative one,

X 3 = C If C is negative, X has three solutions (only one of which is real and the other two are imaginary). In middle school, students are generally forced to accept the wrong view that X 3 = C has only one root. If you insist on the correct view of 1 real root +2 imaginary roots, the college entrance examination will miscalculate you. )

Therefore, in fact, the root number n is a function and the inverse transformation of the function f (x) = x n (because this function is not single-valued, x n = c is n solutions, unless c=0, so according to the regulations, the most representative solution is selected as the principal value to define the root number n).