Multiple Choice Question (MCQ)

Which of the following is equal to \sqrt{9-6\sqrt{2} } +\sqrt{9+6\sqrt{2} }

  1. ×

    3\sqrt{2}

  2. 2\sqrt{6}

  3. ×

    \dfrac{7\sqrt{2} }{2}

  4. ×

    3\sqrt{3}

  5. ×

    6

Collected in the board: Square Root

Steven Zheng posted 3 weeks ago


Answer

  1. \sqrt{9-6\sqrt{2} } +\sqrt{9+6\sqrt{2} }

    =\sqrt{(\sqrt{9-6\sqrt{2} } +\sqrt{9+6\sqrt{2} })^2}

    =\sqrt{9-6\sqrt{2}+9+6\sqrt{2}+2\sqrt{9-6\sqrt{2}}\sqrt{9+6\sqrt{2}}}

    =\sqrt{18+2\sqrt{81-72}}

    =\sqrt{24}

    =2\sqrt{6}

Steven Zheng posted 3 weeks ago

Scroll to Top