Toán $\sqrt{13+6\sqrt{4+\sqrt{9-4\sqrt{2} } }}$ 06/07/2021 By Mary $\sqrt{13+6\sqrt{4+\sqrt{9-4\sqrt{2} } }}$
`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` Trả lời
Đáp án: $3\sqrt2 + 1$ Giải thích các bước giải: $\begin{array}{l}\sqrt{13 + 6\sqrt{4 + \sqrt{9 – 4\sqrt2}}}\\ =\sqrt{13 + 6\sqrt{4 + \sqrt{(2\sqrt2 – 1)^2}}}\\ = \sqrt{13 + 6\sqrt{3 + 2\sqrt2}}\\ = \sqrt{13 +6\sqrt{(\sqrt2 + 1)^2}}\\ = \sqrt{13 + 6(\sqrt2 + 1)}\\ = \sqrt{19 + 6\sqrt2}\\ = \sqrt{(3\sqrt2 + 1)^2}\ = 3\sqrt2 + 1\end{array}$ Trả lời
`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`
Đáp án:
$3\sqrt2 + 1$
Giải thích các bước giải:
$\begin{array}{l}\sqrt{13 + 6\sqrt{4 + \sqrt{9 – 4\sqrt2}}}\\ =\sqrt{13 + 6\sqrt{4 + \sqrt{(2\sqrt2 – 1)^2}}}\\ = \sqrt{13 + 6\sqrt{3 + 2\sqrt2}}\\ = \sqrt{13 +6\sqrt{(\sqrt2 + 1)^2}}\\ = \sqrt{13 + 6(\sqrt2 + 1)}\\ = \sqrt{19 + 6\sqrt2}\\ = \sqrt{(3\sqrt2 + 1)^2}\ = 3\sqrt2 + 1\end{array}$