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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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