This section is an exploration of radical functions, their uses and their mechanics.

By the end of this chapter students should be able to:
  • Determine the domain of a given radical function.
  • Understand the fundamental difference between even and odd radicals.
  • Understand and use radicals as an inverse to a polynomial term.

We aim to answer the following questions in this section:

  • What is a radical function, and why do they appear?
  • What role do inverse functions play in models?
  • How do you remove a radical from an equality and what consequences might occur as a result?

In general we will need to be able to accomplish the following mechanical skills involving radicals:

  • Simplify numerical radicals
  • Identify types of radicands so we know when we can, or can’t, simplify.
  • Remove radicals from an equation in order to solve for a variable inside the radical.
  • Identify the fundamental differences between even and odd radicals.
  • Understand when we need to use the dreaded and when we don’t.
  • Understand radicals as functions versus operations