Surds worsksheet

it goes with the other surds revision notes sheet i uploaded earlier

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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 × 144 .
15
2. a) By rationalising the denominator, simplify .
5
( )
2
b) Show that 3 + 12 = 27.
i i 46
3. a) Prove that 0.4 6 = .
99
i i
b) Hence express 0.34 6 as a fraction.
4. a) Write 600 + 54 in the form p 6 where p is an integer.
600 + 54
b) Hence write in the form q .
338
You may use the fact that 338 = 2 × 132.
1
5. a) Rationalise and simplify .
8
12 + 108
b) By simplifying 12 + 108 , write in the form a b where a and b
8
are integers.
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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 fraction in its simplest form.
7. a) Simplify 18 + 32 .
1
b) Rationalise .
6
8. a) You are given that 12 + 27 = a 3 where a is an integer.…read more

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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
( ) =( ) ( )
2
b) 3 + 12 3 + 12 × 3 + 12 = 3 + 36 + 36 + 12
= 3 + 6 + 6 + 12
= 27.
3.…read more

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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 solution to question 3a).
i i 64 32
0.0 6 4 = = .
990 495
7.…read more

Comments

daviesg

Excellent set of questions and answers on surds and recurring decimals

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