Rationalizing the Denominator

• Rationalizing the denominator


  Multiplying the denominator by an appropriate expression to make the denominator a perfect square or perfect nth power
• Steps to rationalize the denominator

  1. Identify if the denominator contains a radical

  2. Multiply the numerator and denominator by the conjugate of the denominator (if a binomial)

  3. Simplify the resulting expression
• Rationalizing the denominator

  • 1 over square root of 25
  • 3 over square root of 49
  • 3 over square root of 1497
  • 2 over 3 square root of 4
  • 1 over square root of 121
  • Square root of 2 over 121
  • Negative square root of 36 over square root of 64
  • Square root of 11 over negative square root of 36
  • Negative 3 over negative square root of 9
  • Negative square root of 16 over 144
• Conjugate


  A binomial with the same terms but opposite sign
• Rationalizing denominators with variables

  • 2 square root of x over square root of x
  • Square root of 2x over square root of y
  • 1 over square root of 3ab
  • Square root of 3m over 2n
  • Square root of 5a over square root of b
  • Square root of 8x over square root of 3y
  • 3 square root of 3 over square root of 6m
  • 4 square root of 2 over square root of 20p
  • 4 over 3 square root of 2x
• Index


  The exponent in a root
• Rationalizing denominators with indices

  • Cube root of 2 times 2 squared
  • Fifth root of 32 over x