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GCSE MATHEMATICS Higher Tier, topic sheet.
SURDS and RECURRING DECIMALS

a a
Rule i) a × b = ab . =
Rule ii) .
b b
Note that there are no rules involving square-roots and addition /
subtraction!




1. Find the values of:

a) 25 + 144

b) 25 ×…

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6. a) Expand and simplify ( 2 + 3 3 )( 4 2 )
3 .
Give your answer in the form a + b 2 + c 3 + d 6 , where a, b, c and d are
integers.

i i
b) Write 0.0 6 4 as a…

Page 3

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SOLUTIONS / ANSWERS.
1. a) 25 + 144 = 5 + 12 = 17.

b) 25 × 144 = 25 × 144 = 5 × 12 = 60.

15 15 5 15 5
2. a) = × = =3 5.
5 5 5 5


( ) =( ) ( )…

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6. a) Take care with this!
(2 + 3 3 4 2 3 )( ) = 8 2 2 3 + 12 6 3 9
= 8 2 2 3 + 12 6 3 × 3
= 9 + 8 2 2 3 + 12 6 .

b) See the…

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daviesg

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Excellent set of questions and answers on surds and recurring decimals

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