Introduction to Simplifying Roots

Most mathematical operations have a complementary operation that essentially “undoes” it. Complementary operations are called inverse operations.  Addition has subtraction while multiplication has division, for example.  What if you want to “undo” an exponent? For example if you square [latex]6[/latex] to get [latex]36[/latex], how can you get back to [latex]6[/latex]? The complementary operation of exponentiation is a root. The root of a number x is another number, which when multiplied by itself a given number of times, equals x.

Furthermore, did you know that you can take the [latex]6th[/latex] root of a number? You have probably heard of a square root, written [latex]\sqrt{}[/latex], but you can also take a third, fourth and even a [latex]5,000th[/latex] root (if you really had to). In this lesson we will learn how a square root is defined and then we will build on that to form an understanding of nth roots.  We will also introduce cube roots and use factoring and rules for exponents to simplify mathematical expressions that contain roots.

In particular, we will learn how to:

  • Define and evaluate square roots
  • Simplify square roots with variables
  • Define and simplify cube roots
  • Define and evaluate nth roots
  • Estimate roots that are not perfect


Did you have an idea for improving this content? We’d love your input.

Improve this pageLearn More