Addition-and-Subtraction-of-Radicals

Addition and Subtraction of Radicals

Key Concepts

  • Radicals can only be added or subtracted if they are similar (same radicand and index).

Objectives

  • Identify parts of a radical expression.

  • Differentiate like from unlike radicals.

  • Simplify radicals before addition or subtraction.

  • Perform addition and subtraction of radical expressions.

Parts of a Radical

  • Radical Symbol: Represents the root.

  • Index: Implies square root if not shown; is 2 when indicated.

  • Radicand: The expression inside the radical.

  • Coefficient: Number in front of a radical (e.g., 5 in 5√7).

Like Radicals

  • Same index and radicand (e.g., 3√7 and 5√7).

Unlike Radicals

  • Different radicands or indices (e.g., 3√5 and 2√7).

Simplifying Radicals

  • Examples: √12 = 2√3, √54 = 3√6, √20 = 2√5.

Addition of Radicals

  • Example: 8√21 + 2√21 = 10√21.

Subtraction of Radicals

  • Example: 9√11 - 4√11 = 5√11.