## SURDS EXERCISE 1.3.2 – Class IX

1. Simplify the following using laws of indices:

(i) (16)-0.75 x (64)4/3

(16)-0.75 x (64)4/3                              [16 = 24 ]

= (24)-0.75 x (24)4/3                         [64 = 26 ]

= 24 x -3/4 x 26 x 4/3

= 2-3 x 28

= 25

= 32

(ii) (0.25)0.5 x (100)-1/2

(0.25)0.5 x (100)-1/2

= (0.25)1/2 x (1/100 )1/2

= (0.25)1/2 x (1/102 )1/2

= (0.5) x ( 1/10 )

= ( 5/10 ) x ( 1/10)

= 5/100

= 𝟏/𝟐𝟎

(iii) (6.25)0.5 x 102 x (100)-1/2 x (0.01)-1

= ( 625/100 )1/2 x 102 x (1/10)1/2 x ( 1/100 )-1

= ( 25/10 )1/2 x 102 x (1/10 )1/2 x (1/100)-1

= ( 252/10 )1/2 x 102 x (1/102 )1/2 x (100)1

= ( 25/10 ) x 100 x 1 10 x 100

= 2500

(iv) (3-1/2 x 2-1/3) ÷ (3-3/4 x 2-5/6)

= 3−1/2× 2−1/3 3−3/4× 2−5/6

= 3-1/2+3/4 x 2-1/3+5/6

= 31/4 x 23/6

= 31/4 x 21/2

= 31/4 x 21/4

=(3 × 22)1/4

= (3 × 4)1/4

= 𝟏𝟐1/4

1. Find the value of the expression.

[ 31/3 {5-1/2 x 3-1/3 x (2252)1/3}1/2]6

Solution:

= [ 31/3 {5-1/2x-1/2 x 3-1/3x1/2 x (2252)2/3x1/2]6

= [ 31/3 {5-1/4 x 31/6 x (2252)-2/6]6

= [ 31/3 x 6 {51/4 x 6 x 31/6 x 6 x (2252)-2/6 x 6]

= [ 32 x 51/4 x 6 x 31/6 x 6 x 2252-2/6 x 6]

= [32 x 53/2 x 31 x 225-2]

= [32 x 52/3 x 31 x 15-4]

= [32 x 5-2/3 x 31 x 3-4 x 5-4]

= [32 + 1 – 4 x 53/2 – 4]

= 1/31 x 1/55/2

= 1/31  x 1/55/2

= 1/31  x 1/√55

= 1/3 x 1/√3125

= 1/3√3125

1. Simplify:

[{(35/2 x 53/4) ÷ 2-5/4} ÷ {16 / (52 x 21/4 x 31/2)}]1/5

Solution:

= [{(35/2 × 53/4) ÷ 2−5/4} ÷ {16÷ (52× 21/4× 31/2)}] 1/5

= [{(35/2 × 53/4)/(2−54) ÷ 16/(52× 21/4× 31/2)}] 1/5

= [(35/2 × 53/4)/(2−54) ÷ (52× 21/4× 31/2)/24]1/5

= [(35/2 × 53/4 × 52/1 × 21/4 × 31/2)/(2−5/4 × 24 )]1/5

= [21/4 × 35/2 + 1/2 × 53/4 + 2/1/2−5/4 + 4/1]1/5

= 21/4 × 35/2 + 1/2 × 511/4/211/4]1/5

= [21/4 4/11 × 33 × 511/4 ] 1/5

= [210/4 × 1/5 × 33 × 1/5 × 511/4 + 1/5]

= 21/2 × 31/5 × 511/20