Operations with radicals

Math

Definition

The rules for adding, subtracting, multiplying, and dividing expressions containing square roots or other radicals. Like terms (same radicand and index) can be combined, and multiplication/division follow product and quotient rules.

Examples

  • 3√2 + 5√2 = 8√2 (adding like radicals)
  • √3 × √12 = √36 = 6 (multiplying radicals)
  • Rationalizing a denominator: 1/√2 = √2/2
Key Fact

√a × √b = √(ab); √a / √b = √(a/b); can only add/subtract radicals with the same radicand

Related Terms

Simplifying radicals Nth roots Rational exponents

Study This Concept

Practice operations with radicals with free review games in these units:

Algebra 1 Unit 9: Radical Expressions