- Find which is larger:
(i) 3∛𝟑 and 4∜𝟒
∛(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
4∜𝟒 is greater 3∛𝟑
- 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)
- 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
- 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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