Surds

• Rationalizing the denominator

  1. Multiply the top and bottom of the fraction by the denominator

  2. Change the sign of the denominator if it has two terms
• Rational number


  A number that can be expressed as a fraction
• Irrational number


  A number that cannot be expressed as a fraction
• Fractions to rationalize

  • 4 over root 5
  • 7 over 2 plus root 3
• Rationalizing 4 over root 5


  Multiply top and bottom by root 5
• Rationalizing 7 over 2 plus root 3


  1. Multiply top and bottom by 2 minus root 3

  2. Simplify the denominator
• More fractions to rationalize

  • 6 over root 3
  • 7 plus root 5 over root 5 minus 1
• Rationalizing 6 over root 3


  Multiply top and bottom by root 3
• Rationalizing 7 plus root 5 over root 5 minus 1


  1. Multiply top and bottom by root 5 plus 1

  2. Simplify the numerator and denominator
• The final answer should be in the form a plus b root 5, where a and b are positive integers