Comparison of Surds

CAT 2006 Slot 1 · QA · Easy · Quantitative Aptitude

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Which among 21/22^{1/2}, 31/33^{1/3}, 41/44^{1/4}, 61/66^{1/6} and 121/1212^{1/12} is the largest?

  1. A.

    2^(1/2)

  2. B.

    3^(1/3)

  3. C.

    4^(1/4)

  4. D.

    6^(1/6)

  5. E.

    12^(1/12)

Answer

3^(1/3)

Explanation

Raise all numbers to the 12th power (LCM of denominators 2, 3, 4, 6, 12 is 12):

  1. (21/2)12=26=64(2^{1/2})^{12} = 2^6 = 64
  2. (31/3)12=34=81(3^{1/3})^{12} = 3^4 = 81
  3. (41/4)12=43=64(4^{1/4})^{12} = 4^3 = 64
  4. (61/6)12=62=36(6^{1/6})^{12} = 6^2 = 36
  5. (121/12)12=121=12(12^{1/12})^{12} = 12^1 = 12

81 is the largest, so 31/33^{1/3} is the largest.

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