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$$2\root 3 \of {32} - 3\root 3 \of 4 + \root 3 \of {500} = ?$$

$$2\root 3 \of {32} - 3\root 3 \of 4 + \root 3 \of {500} = ?$$ Correct Answer $$6\root 3 \of 4 $$

$$\eqalign{ & 2\root 3 \of {32} - 3\root 3 \of 4 + \root 3 \of {500} \cr & = 2\root 3 \of {{2^3} \times 4} - 3\root 3 \of 4 + \root 3 \of {{5^3} \times 4} \cr & = 2 \times 2\root 3 \of 4 - 3\root 3 \of 4 + 5\root 3 \of 4 \cr & = 9\root 3 \of 4 - 3\root 3 \of 4 \cr & = 6\root 3 \of 4 \cr} $$

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