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square root

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Summer Clouds moderators
19/07/2017 at 09:07
Answers
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The number \(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)  equals :
A. \(\sqrt{6}\)
B. \(2\sqrt{3}\)
C. \(1+\sqrt{3}\)
D. \(\sqrt{3}-1\)

square root

  • ...
    Aim Egst 19/07/2017 at 10:46

    \(A=\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)

    \(A^2=2-\sqrt{3}+2+\sqrt{3}+2\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}\)

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

    \(A^2=4+2\sqrt{4-3}=4+2=6\)

    \(\Rightarrow A^2=6\Rightarrow A=\sqrt{6}\)

    Select A

    Selected by MathYouLike
  • ...
    FA KAKALOTS 08/02/2018 at 21:58

    A=√2−√3+√2+√3

    A2=2−√3+2+√3+2√(2−√3)(2+√3)

    A2=4+2√22−√32

    A2=4+2√4−3=4+2=6

    ⇒A2=6⇒A=√6

    Select A

  • ...
    lê đức anh 10/01/2020 at 13:27

    câu trả lời là A

    hk tốt


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