Multiple Choice Question (MCQ)

If a= {7-4\sqrt{3} }

​ find the value of \sqrt{a} +\dfrac{1}{\sqrt{a} }

  1. 4

  2. ×

    9

  3. ×

    11

  4. ×

    14

Collected in the board: Square Root

Steven Zheng posted 11 hours ago

Answer

  1. a= {7-4\sqrt{3} }

    =2^2-4\sqrt{3}+(\sqrt{3} )^2

    =(2-\sqrt{3})^2

    Therefore

    \sqrt{a} =2-\sqrt{3}

    Reciprocal of \sqrt{a}

    \dfrac{1}{\sqrt{a} }=\dfrac{1}{2-\sqrt{3} }

    =\dfrac{1}{2-\sqrt{3} } \cdot \dfrac{2+\sqrt{3}}{2+\sqrt{3} }

    =2+\sqrt{3}

    Addition of \sqrt{a} and \dfrac{1}{\sqrt{a} }

    \sqrt{a} +\dfrac{1}{\sqrt{a} } = 4

    So option A is the right choice

Steven Zheng posted 11 hours ago

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