The square root of a negative number can be described as: (Select all that apply.) Imaginary number Extraneous Number Undefined Real number

1. We start by recalling that the square root of a negative number is not defined within the real numbers. 2. Instead, mathematicians define a new number, \(i\), called the imaginary unit, where \[ i^2 = -1. \] 3. Using this definition, any square root of a negative number can be expressed in the form \[ \sqrt{-a} = i\sqrt{a}, \] where \(a > 0\). 4. Therefore, the square root of a negative number is not a real number, nor is it an extraneous number (a term used for solutions that arise during the process of solving an equation but do not satisfy the original equation). 5. Although one might say that the square root of a negative number is "undefined" in the context of real numbers, within the broader context of complex numbers it is defined as an imaginary number. The correct selection is: - Imaginary number