SURDS EXERCISE – 1.3.4 – Class 9

  1. Find which is larger:

(i) 3𝟑 and 4𝟒

∛(3×32)                                                        4×424

= 27 x 3                                                   = 256 x 4

= 81                                                             = 1024

= ((81)4)1/12                                                  = ((1024)4)1/12

= (43046721)1/12                                         = (1073741824)1/12

4𝟒 is greater 3𝟑


  1. Compare the following and decide which is larger.

(i) (∜(30))1/7 and ∛(281/10)

(281/10) 1/3 = (281/10)1/3 = 281/30

(301/4) 1/7 = (301/4)1/7 = 301/28

LCM of 30 and 28 is 420

(281/10)1/3 = 281/30 = (281/14)1/420

(301/4) 1/7 = 301/28 = (3015)1/420

2814 =22 x 714 = 228 x 714

3015 = (5 x 6)15 = 515 x 615

Comparing the 2 numbers we conclude

3015 > 2814

(∜(30))1/7 > ∛(281/10)

 

(ii) √(∜8)  and ∛(∛9)

√(∜8) = (81/4)1/2 = 81/8 = 23/8          [8 = 23]

∛(∛9) = (91/3)1/3 = (32/3)1/3 = 32/9

LCM of 8 and 9 is 72

√(∜8)  = 23/8 = (23/8)9/9 = 227/72 = (227)1/72

∛(∛9) = 32/9 = (32/9)8/8 = 316/72 = (316)1/72

By comparing we find that (227) is larger than 316.

Hence √(∜8)   > ∛(∛9)


  1. Write the following in ascending order:

√𝟐 , 𝟑𝟑 , 𝟔1/6

21/2 , 31/3 , 61/6

LCM of 2, 3 and 6 is 6

21/2 = 23/6 = (23)1/6 = 81/6

31/3 = 32/6 = (33)1/6 = 91/6

61/6 = 63/6 = (6)1/6 = 61/6

Ascending order is 61/6  , 21/2, 31/3


  1. Write the following descending order:

√(𝟔) , (∜𝟏𝟐) , (∜𝟖)

(61/3)1/2 , (121/4)1/3 , (81/4)1/2

61/6, 121/12 , 81/8

LCM of 6, 12, 8 is 24

64/24, 122/24, 83/24

(64)1/24, (122)1/24, (83)1/24

(1296)1/24, (144)1/24, (512)1/24

Descending order is √(𝟔)  , √ (∜𝟖)  , ∛(∜𝟏𝟐)


 

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