Multiple Choice Question (MCQ)

Rationalizing the denominator of \dfrac{1}{\sqrt{7}-\sqrt{6} } gives

  1. ×

    \dfrac{\sqrt{7}+\sqrt{6} }{\sqrt{7}-\sqrt{6} }

  2. ×

    \dfrac{\sqrt{7}-\sqrt{6} }{\sqrt{7}+\sqrt{6} }

  3. \sqrt{7}+\sqrt{6}

  4. ×

    \sqrt{7}-\sqrt{6}

Collected in the board: Square Root

Steven Zheng posted 4 hours ago

Answer

  1. Multiply both nominator and denominator with \sqrt{7}+\sqrt{6} to rationalize the denominator

    \dfrac{1}{\sqrt{7}-\sqrt{6} }

    =\dfrac{1}{\sqrt{7}-\sqrt{6}}\cdot \dfrac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}}

    =\dfrac{\sqrt{7}+\sqrt{6}}{(\sqrt{7} )^2-(\sqrt{6} )^2}

    =\dfrac{\sqrt{7}+\sqrt{6}}{7-6}

    =\sqrt{7}+\sqrt{6}

    Therefore, C is right choice

Steven Zheng posted 4 hours ago

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