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Which of the following statement(s) is are true I (65)1 6...

This question belongs to Arithmetic Ability Surds And Indices
Surds and Indices
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Which of the following statement(s) is/are true?
I. (65)1/6 > (17)1/4 > (12)1/3
II. (17)1/4 > (65)1/6 > (12)1/3
III. (12)1/3 > (17)1/4 > (65)1/6

Answer & Solution
Correct Answer: Option B
(65)1/6
(17)1/4
(12)1/3
LCM of 4, 6, 3 = 12
∴ (652)1/12 = (4225)1/12 . . . . . . (I)
(173)1/12 = (4913)1/12 . . . . . . (II)
(124)1/12 = (20736)1/12 . . . . . . (III)
From equation (I), (II), (III) we can see that only (III) statement follows.
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