# Surds

Description
Surds exam questions for C1.1 Edexcel AS Level Mathematics
Categories
Published

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
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

Jul 23, 2017

#### Che492 Handouts

Jul 23, 2017
Search
Similar documents

View more...
Tags