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Surds exam questions for C1.1 Edexcel AS Level Mathematics
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  Surds & Indices  Core 1 is a NON CALCULATOR  module Chapter 1Algebra : Core 11.1 Square Roots without a calculatorExample :  Find  2704  1.2 Square Free Any number which is not prime can be written as a unique product of primes.For example,120 =    2  3 ×    3 ×    5Mathematicians talk of the decomposition  of 120 into a product of primes.There is another decomposition of 120 that is useful, and it revolves arounddeciding what the biggest square number that will divide into 120 exactly is. Reminder:  Square Numbers = { 1, 4, 9, 16, 25, 36, ..... }As 4 is the biggest square number thet divides into 120 we have that,120 =    4 ×    30Notice that no square number, other than 1, will divide into 30.Thus 30 is termed square-free or, if you are a cool mathematician,       Free.So, our new decomposition takes a number that is not       Free and writes it asa square number multiplied by a square free number.  Non =× Free Example :  Write in the form a    120   p  where a  &  p  are integersand  p  is       FREE.  1.3 ExerciseQuestion 1. Square root the following square numbers. ( i ) 3969 ( ii ) 5625 Question 2. Each of the following numbers is not square free.Decompose them into a square number multiplied by a square free number. ( i ) 8 ( ii ) 27 ( iii ) 48 ( iv ) 98 ( v ) 56 ( vi ) 242 ( vii ) 320  Question 3 .Write each of the following in the form a     p  where a  &  p  are integersand  p  is       FREE. HINT :  Use your earlier answers to Question 2 . ( i )( ii )  8  27  ( iii )( iv )  48  98  ( v )( vi )  56  242  ( vii )  320  Question 4. Each of the following numbers is not square free.Decompose them into a square number multiplied by a square free number. ( i ) 504 ( ii ) 1452  ( iii ) 6750 ( iv ) 5346 Question 5 .Write each of the following in the form a     p  where a  &  p  are integersand  p  is       FREE. HINT :  Use your earlier answers to Question 4 . ( i )( ii )  504  1452  ( iii )( iv )  6750  5346  Question 6. What is the cube root of 1728 ?  i .  e . 3  1728  These lesson notes are available from www.piLEARN.comThey may be freely duplicated and distributed but copyright remains with the author.© 2013 Martin Hansen
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