$\sqrt{13+6\sqrt{4+\sqrt{9-4\sqrt{2} } }}$

Question

$\sqrt{13+6\sqrt{4+\sqrt{9-4\sqrt{2} } }}$

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Philomena 8 tháng 2020-10-15T17:57:41+00:00 2 Answers 79 views 0

Answers ( )

  1. Đáp án:

    $3\sqrt2 + 1$

    Giải thích các bước giải:

    $\begin{array}{l}\sqrt{13 + 6\sqrt{4 + \sqrt{9 – 4\sqrt2}}}\\ =\sqrt{13 + 6\sqrt{4 + \sqrt{(2\sqrt2 – 1)^2}}}\\ = \sqrt{13 + 6\sqrt{3 + 2\sqrt2}}\\ = \sqrt{13 +6\sqrt{(\sqrt2 + 1)^2}}\\ = \sqrt{13 + 6(\sqrt2 + 1)}\\ = \sqrt{19 + 6\sqrt2}\\ = \sqrt{(3\sqrt2 + 1)^2}\ = 3\sqrt2 + 1\end{array}$

  2. `sqrt{13 + 6\sqrt{4 + \sqrt{9 – 4\sqrt{2}}}}`

    `= sqrt{13 + 6\sqrt{4 + \sqrt{(2\sqrt{2} – 1)^2}}}`

    `= sqrt{13 + 6\sqrt{3 + 2\sqrt{2}}`

    `= sqrt{13 + 6\sqrt{(\sqrt{2} + 1)^2}}`

    `= sqrt{19 + 6\sqrt{2}}`

    `= sqrt{(3\sqrt{2} + 1)^2}`

    `= 3sqrt{2} + 1`

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