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Number of irrational terms in (a^(1/p) + b^(1/q))^n

The same question, asked 2 times: 2021 Paper 5*, 2021 Paper 15. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 5

    72
    If nn is the number of irrational terms in the expansion of (31/4+51/8)60\left( 3^{1/4}+5^{1/8} \right)^{60}, then (n−1)(n- 1) is divisible by:

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  2. Question 2

    2021 Paper 15

    57
    Find the number of irrational terms in (213+314)12\left( 2^{\frac{1}{3}}+3^{\frac{1}{4}} \right)^{12}.