Question

Свойства корня n-ой степени.

Answer 1

Вот тебе, если не правильно удали коментарий 

Answer 2

Properties of the n-th Root

The properties of the n-th root, where n is a positive integer, include:

1. Definition: - The n-th root of a number a is denoted as \[\sqrt[n]{a}\]. - For a non-negative number a (\[a \geq 0\]), \[\sqrt[n]{a}\] is the unique non-negative number x such that \[x^n = a\]. - If a < 0, then \[\sqrt[n]{a}\] is the unique negative number x such that \[x^n = a\].

2. Examples: - For example, the 4th root of 81 is 3, because 3^4 = 81. - The n-th root of a to the power of n is a, denoted as \[a^{\frac{1}{n}} = \sqrt[n]{a}\].

3. Properties: - The n-th root of a non-negative number is always non-negative. - The n-th root of a negative number is always negative. - If n is even, then the n-th root of a negative number is not a real number. - If n is odd, then the n-th root of a negative number is a real number. - The n-th root of 0 is 0. - The n-th root of 1 is 1. - The n-th root of -1 depends on the value of n. For odd n, \[\sqrt[n]{-1} = -1\], and for even n, \[\sqrt[n]{-1}\] is not a real number.

4. Additional Information: - The n-th root is used in various mathematical and scientific contexts, such as in solving equations, simplifying expressions, and in the calculation of geometric and physical quantities.

These properties and definitions are fundamental to understanding the behavior and characteristics of the n-th root in mathematics and its applications in various fields.