© Cengage Learning Australia Pty Ltd 2014 MAT10NAWK10095 Number and Algebra: Real numbers www.nelsonnet.com.au 1 of 3 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 1 3 ___________ b 2 5 ___________ c 6 6 ___________ d 35 7 ___________ e 7 2 5 ___________ f 12 5 3 ___________ g 10 3 2 ___________ h 10 6 ___________ i 7 5 ___________ j 3 4 8 2 ___________ k 2 5 7 2 1 ___________ l 2 6 3 1 ___________