Addition and Subtraction of Radicals

• Differentiating like radicals from unlike radicals

  1. Identify same index and same radicand

  2. Identify different index or different radicand
• Adding and subtracting radical expressions

  1. Use distributive property

  2. Combine like radicals
• Like radicals


  Radicals with same index and same radicand
• Unlike radicals

  Radicals with different index or different radicand
• Like radicals

  • Square root of 2
  • Square root of 6
• Simplifying radical expressions

  1. Factor radicands to find perfect squares

  2. Simplify square roots of perfect squares

  3. Combine like radicals
• Simplifying radical expressions

  • Square root of 200 = 10 square root of 2
  • Square root of 50 = 5 square root of 2
  • Square root of 8 = 2 square root of 2
• Rationalizing denominators involves multiplying by the conjugate to eliminate the radical in the denominator
• Rationalizing denominators

  • Square root of 2 + square root of 1/2 = 3 square root of 2 / 2
  • Square root of 3 - square root of 1/3 = 2 square root of 3 / 3
• The LCD (Least Common Denominator) is used when adding/subtracting radical expressions with different denominators