Question
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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