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Unit 4 - Radical Expressions and Equations

Radical expressions (and equations) involve square roots, cube roots, or any other nth roots. The n in nth root is called the index. Whatever expression is under the radical symbol represents the radicand.

Radical expressions can be simplified using factoring and combining of radicals to cancel out any roots.

Radical expressions further simplify following the same rules as other terms such as combining like terms. Radical expressions are considered simplified if:
  • no radicands have perfect square factors other than 1
  • no radicands contain fractions
  • no radical appear in the denominator of a fraction
Solving radical equations is possible using the inverse of nth roots which is raising to the nth power. Generally speaking, nth roots are canceled out in the following way:
Radical equations can be used to model numerous real world applications.

Challenge Activity
  • Prerequisite Understanding
    • coming soon...
  • 4.A. Simplifying Radicals

  • 4.B. Operations with Radicals

    • 4.C. Solving Radical Equations
    • 4.D. Applications of Radicals