Radical Expressions

In this section, we review radical expressions: square roots, cube roots, and higher index roots. We begin with the most common root: the square root. The square root of a number is any number that multiplies by itself to give the number. For example, the square root of 4, is (-2) and (+2). Since (-2)(-2)=4, and (2)(2)=4. We then move into more advanced roots, such as: cube roots, fourth roots, and fifth roots. The concept is the same. For a cube root, we are looking for a number that multiplies by itself three times to give the number. For example, the cube root of 8 is 2: (2)(2)(2)=8. We will run across several special scenarios when working with roots. For the purposes of notation, every even indexed root has a principal root and a negative root. To ask for (-2) as the answer for the square root of 4, we ask for the negative square root of 4. We indicate this by placing a negative in front of the square root symbol. Additionally, we must be aware that with even indexed roots, we can’t have a negative radicand (number under the radical symbol). When this occurs, we give our answer as “no real solution”. In the coming lessons, we will learn how to deal with this scenario using the complex number system.