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3.4 - nth Roots and Radical Expressions

3.4 - nth Roots and Radical Expressions

Author: Kyle Webb
  • Denote nth roots using the index and the radicand
  • Find principal roots
  • Performs operations with Radical Expressions
    • Product Property of Radicals
    • Quotient Property of Radicals
  • Use conjugates to eliminate radicals in the denominator of an expression

You have some experience working with roots other than square roots, and in this section we will examine other roots, known as nth roots, in more detail.  We will also explore operations radical expressions both with square roots and with nth roots. 


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Operations of Radical Expressions

We will need to remember these two basic properties of radicals.

Product Property of Radicals

n-th root of a b end root equals n-th root of a cross times n-th root of b

Quotient Property of Radicals

n-th root of a over b end root equals fraction numerator n-th root of a over denominator n-th root of b end fraction, as long as all roots are defined and b not equal to 0

Radical Expressions with Higher Roots

More Simplifying Radical Expressions


Stop here if you're completely part 1 of the OneNote.

How to Rationalize a Denominator