Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(−17)^2

Key Concepts

Square Root Function

The square root function, denoted as √x, is defined as the value that, when multiplied by itself, gives x. For non-negative numbers, the square root is a real number. However, when dealing with negative numbers, the square root is not defined in the set of real numbers, leading to complex numbers instead.

Exponentiation

Exponentiation is a mathematical operation involving two numbers, the base and the exponent. In the expression (−17)^2, the base is −17 and the exponent is 2, meaning that −17 is multiplied by itself. This results in a positive value, as squaring any real number, whether positive or negative, yields a non-negative result.

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, typically expressed in the form a + bi, where 'a' is the real part and 'bi' is the imaginary part. The square root of a negative number, such as √(−x), results in an imaginary number, indicating that the solution is not a real number but rather exists in the complex number system.