Title: Mar 3­04:08 p.m. (1 of 25)
Surds
    By the end of the lesson you should be able to:



   • Distinguish between  the different sets of numbers.

   • Simplify expressions involving surds.

   • Rationalise fractions with surds in the denominator.




Title: Mar 3­04:08 p.m. (2 of 25)
Sets of numbers

                 = {1, 2, 3, 4,...}                Natural numbers

                     = {...,­2,­1,0 , 1 ,2 ,3,...}
                                              Integer numbers
              = {any number that can be expressed as a fraction}
                                          Rational  numbers

                                0.2                                50 
                       terminating decimals                        whole 
                                              recurring decimals   numbers
      fractions


Title: Mar 3­04:08 p.m. (3 of 25)
Irrational numbers: cannot be expressed as 
        fractions

        π                      4.01001000100001...




                     =                ∪ {Irrationals}
              Real numbers

Title: Mar 3­04:08 p.m. (4 of 25)
Title: Mar 3­04:08 p.m. (5 of 25)
Circle the irrational numbers:


    1.3




Title: Mar 3­04:08 p.m. (6 of 25)
Rational or irrational?




Title: Mar 3­04:08 p.m. (7 of 25)
n = 3
   Ring any of these which are rational when 




Title: Mar 3­04:08 p.m. (8 of 25)
When a root cannot be found exactly, then the 
      root is called a surd.




                      Surds or Radicals




Title: Mar 3­04:08 p.m. (9 of 25)
Irrational numbers on the number line




Title: Mar 3­04:08 p.m. (10 of 25)
Title: Mar 3­04:08 p.m. (11 of 25)
Basic rules:
      If a and b are positive:




Title: Mar 3­04:08 p.m. (12 of 25)
Title: Mar 3­04:08 p.m. (13 of 25)
Simplify:




Title: Mar 3­04:08 p.m. (14 of 25)
Title: Mar 3­04:08 p.m. (15 of 25)
Title: Mar 3­04:08 p.m. (16 of 25)
end first lesson:




Title: Mar 3­04:08 p.m. (17 of 25)
Title: Mar 3­04:08 p.m. (18 of 25)
Title: Mar 3­04:08 p.m. (19 of 25)
Title: Mar 3­04:08 p.m. (20 of 25)
Simplification of surds




Title: Mar 3­04:08 p.m. (21 of 25)
Operations with surds




Title: Mar 3­04:08 p.m. (22 of 25)
Multiplication of surds




Title: Mar 3­04:08 p.m. (23 of 25)
http://www.mymaths.co.uk/gold/Alevel/core1/indices/indices4Surds1.html




                                      Surds worksheet.doc




Title: Mar 3­04:08 p.m. (24 of 25)
http://www.maths­bingo.com




                                     See next exercise at the end of the lesson




Title: Mar 3­04:08 p.m. (25 of 25)
Attachments



   Surds worksheet.doc

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