10th Class Mathematics Real Numbers Question Bank Real Numbers

  • question_answer The descending order of the surds \[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4}\]is,__

    A) \[\sqrt[6]{4},\sqrt[6]{3},\sqrt[3]{2}\]             

    B) \[\sqrt[9]{4},\sqrt[3]{2},\sqrt[6]{3}\]

    C)         \[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4}\]    

    D)         \[\sqrt[6]{3},\sqrt[9]{4},\sqrt[3]{2}\]            

    Correct Answer: C

    Solution :

    L.C.M. of 3, 6, 9 is 18. \[\sqrt[3]{2}={{(2)}^{1/3}}={{(2)}^{6/18}}=-{{(64)}^{\frac{1}{18}}}\] \[\sqrt[3]{6}={{(3)}^{1/6}}={{(3)}^{3/18}}={{(27)}^{\frac{1}{18}}}\] Descending order is, \[\sqrt[3]{2}>\sqrt[6]{3}>\sqrt[9]{4}\]


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