Product Rule for Radicals

  • \sqrt [ n ]{ a*b } =\sqrt [ n ]{ a } *\sqrt [ n ]{ b }
  • In plain language, the nth root of a real number is equal to the product of the nth roots of its factor pairs
  • Example: \sqrt { 12 } =\sqrt { 4*3 } =\sqrt { 4 } *\sqrt { 3 }
  • Application: Simplifying radical expressions