Which among ∜10 and ∛8 is greater?

Q: Which among ∜10 and ∛8 is greater?

∜10 and ∛8 = 101/4 and 81/3 Since, LCM of 4 and 3 is 12. ∴ 101/4 = 103/12 = (103)1/12 = (1000)1/12 = 12√1000 and 81/3 = 84/12 = (84)1/12 (4096)1/2 = 12√4096 ∴ 4096 > 1000 Hence, 81/3 >101/4 ∴ ∛8 > ∜10

∛10
∛8
Both are equal
None of these

Correct Answer: ∛8

Explanation:

∜10 and ∛8 = 10^1/4 and 8^1/3
Since, LCM of 4 and 3 is 12.
∴ 10^1/4 = 10^3/12 = (10³)^1/12 = (1000)^1/12 = ¹²√1000
and 8^1/3 = 8^4/12 = (8⁴)^1/12 (4096)^1/2 = ¹²√4096
∴ 4096 > 1000
Hence, 8^1/3 >10^1/4
∴ ∛8 > ∜10

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