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      Question

      src="https://www.ixambee.com/questionimage/SSC%20CGL%20Tier-II/SSC%20CGL%20MT%20-%201%20E%20-%20Q%207.JPG" alt="" />
      A 64 Correct Answer Incorrect Answer
      B 8 Correct Answer Incorrect Answer
      C 1 Correct Answer Incorrect Answer
      D 512 Correct Answer Incorrect Answer

      Solution

      Let: x = √[8 × ∛(64 × √[8 × ∛(64 × ...)])] Start simplifying: x = √(8 × ∛(64 × x)) = √(8 × 4 × x(1/3))              :: [∛64 = 4] = √(32 × x(1/3)) = √32 × x(1/6) = 4√2 × x(1/6) Now solve = x = 4√2 × x(1/6) => x(5/6) = 4√2 => x = (4√2)(6/5) Simplify powers = 4√2 = 22 × 2(1/2) = 2(5/2) => x = (2(5/2))(6/5) = 23 = 8

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