What Are Radicals?

Simplifying radicals

Doing arithmetic with radicals

Simplifying rational exponents

Working with complex numbers

Radicals are the undoing of exponents. In other words, since 2 squared is 4, radical 4 is 2. The radical sign, , is used to indicate “the root” of the number beneath it. If the radical sign has no number written in its leading crook (like this , indicating cube root), then it is the square root of the number under the sign that is being indicated. This chapter is concerned with the terminology and operations involving radical expressions. When operating arithmetically on radicals, the radical behaves as if it were a variable. 

Complex numbers are natural partners of radicals. They result from finding the radical of a negative expression. The imaginary number, i, is used to represent the square root of –1. So, 3 i expresses the simplification of