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CLAT Sample Paper CLAT Sample Paper-2

  • question_answer
    If \[x=3+2\sqrt{2},\] then find the value of \[{{x}^{1/2}}-{{x}^{-1/2}}\].

    A)  \[\frac{1}{2}\]

    B)  \[\sqrt{2}\]

    C)  2

    D)  None of these

    Correct Answer: C

    Solution :

    Given, \[x=3+2\sqrt{2}={{(\sqrt{2}+1)}^{2}}\] \[\Rightarrow \] \[{{x}^{1/2}}=\sqrt{2}+1\] \[\therefore \] \[{{x}^{-1/2}}=\frac{1}{\sqrt{2}+1}=\sqrt{2}-1\] Hence, \[{{x}^{1/2}}-{{x}^{-1/2}}=\sqrt{2}+1-\sqrt{2}+1=2\]


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