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Which is the greatest of √2, ∛3 and ⁶√6?

Competition practiceNumber & Arithmetic
  • A∛3
  • B√2
  • C⁶√6
  • DAll three are equal

Step-by-Step Solution

Bring them to a common index 6: √2 = ⁶√ ⁶√8, ∛3 = ⁶√ ⁶√9 and ⁶√6 stays ⁶√6. Since 9 > 8 > 6, the greatest is ∛3 (≈ 1.442 against 1.414 and 1.348).
Answer: A) ∛3

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