$\sqrt{13+6\sqrt{4+\sqrt{9-4\sqrt{2} } }}$ Question $\sqrt{13+6\sqrt{4+\sqrt{9-4\sqrt{2} } }}$ in progress 0 Môn Toán Philomena 4 years 2020-10-15T17:57:41+00:00 2020-10-15T17:57:41+00:00 2 Answers 91 views 0
Answers ( )
Đáp án:
$3\sqrt2 + 1$
Giải thích các bước giải:
$\begin{array}{l}\sqrt{13 + 6\sqrt{4 + \sqrt{9 – 4\sqrt2}}}\\ =\sqrt{13 + 6\sqrt{4 + \sqrt{(2\sqrt2 – 1)^2}}}\\ = \sqrt{13 + 6\sqrt{3 + 2\sqrt2}}\\ = \sqrt{13 +6\sqrt{(\sqrt2 + 1)^2}}\\ = \sqrt{13 + 6(\sqrt2 + 1)}\\ = \sqrt{19 + 6\sqrt2}\\ = \sqrt{(3\sqrt2 + 1)^2}\ = 3\sqrt2 + 1\end{array}$
`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`