© Cengage Learning Australia Pty Ltd 2014 MAT10NAWK10095 Number and Algebra: Real numbers www.nelsonnet.com.au

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Multiplying and dividing surds

Worksheet

1 Simplify each of these expressions.

a 2 3 3 ___________ b 11 3 7 ___________ c 8 3 2 ___________

d 2 3 10 ___________ e 6 3 3 ___________ f 8 3 8 ___________

g 2 5 3 5 ___________ h 3 7 3 2 ___________ i 5 3 3 5 3 ___________

j 4 6 3 8 ___________ k 3 12 3 2 3 ___________ l 2 15 3 4 5 ___________

m 2 3 3 10 ___________ n 7 2 3 2 7 ___________ o 3 5 3 3 10 ___________

2 Expand and simplify each of these expressions.

a 2( 3 1 3) ___________ b 4(2 2 5 ) ___________ c 3(2 2 1 10) ___________

d 6( 7 1 3 ) ___________ e 5 (4 2 5 ) ___________ f 2 ( 18 1 2) ___________

g 6 (5 2 2 ) ___________ h 3 (7 1 2 ) ___________ i 2 2 ( 10 2 3) ___________

j 10 6 (4 1 3 ) ___________ k 3 3 ( 3 1 6) ___________ l 5 10 (2 2 5 ) ___________

3 Expand and simplify each expression.

a (4 1 5 )(2 1 5 ) _______________ b (3 2 2 )(4 1 2 ) _______________

c (2 3 1 7)( 3 2 1) _______________ d (5 10 2 1)(3 2 10 ) _______________

e (2 1 3 )(2 2 3 ) _______________ f (5 1 7 )(5 2 7 ) _______________

g ( 10 2 6 )( 10 1 6 ) _______________ h (3 2 2 2 )(3 1 2 ) _______________

i (5 1 6 )2 _______________ j ( 3 2 2 )2 _______________

k (4 1 2 )2 _______________ l (3 2 2 5 )2 _______________

4 Rationalise the denominator of each of the following expressions.

a 13

___________ b 25

___________ c 66

___________

d 357

___________ e 72 5

___________ f 125 3

___________

g 103 2

___________ h 106

___________ i 75

___________

j 3 4

82

___________ k 2 5 721 ___________ l

2 63

1 ___________

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© Cengage Learning Australia Pty Ltd 2014 MAT10NAWK10095 Number and Algebra: Real numbers www.nelsonnet.com.au

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Expression i evaluate to three decimal places

ii rationalise the denominator

iii evaluate ii to three decimal places

a12

b23

c 53

d 32 3

e 213 6

f4 2

21

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© Cengage Learning Australia Pty Ltd 2014 MAT10NAWK10095 Number and Algebra: Real numbers www.nelsonnet.com.au

Answers1 a 6 b 77 c 4 d 2 5

e 3 2 f 8 g 10 h 3 14

i 75 j 16 3 k 36 l 40 3

m 6 5 n 14 14 o 45 2

2 a 2 3 1 6 b 8 2 4 5 c 6 2 1 30 d 6 7 1 6 3

e 4 5 2 5 f 6 1 2 2 g 5 6 2 2 3 h 7 3 1 6

i 4 5 2 6 2 j 40 6 1 30 2 k 9 1 18 3 l 10 10 2 25 2

3 a 13 1 6 5 b 10 2 2 c 5 3 2 1 d 16 10 2 53

e 1 f 18 g 4 h 5 2 3 2

i 31 1 10 6 j 5 2 2 6 k 18 1 8 2 l 29 2 12 5

4 a 33

b 2 55

c 6 d 5 7

e 7 510

f 4 35

g 5 2

3 h

153

i 355

j 6 4 24

2 k 2 10 7 221 l

2 3 3 231

5 i ii iii

a 0.707 22

0.707

b 1.155 2 33

1.155

c 2.887 5 33

2.887

d 0.866 32

0.866

e 2.858 7 66

2.858

f 3.828 2 2 1 1 3.828

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