Question

помогите как это решать?

$\sqrt{9 - 4 \sqrt{2} } + \sqrt{17 - 12 \sqrt{2} }$

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Answer 1

$\displaystyle\bf\\1)\\\\\sqrt{9-4\sqrt{2} } =\sqrt{8-4\sqrt{2} +1} =\sqrt{(2\sqrt{2} )^{2} -2\cdot 2\sqrt{2}\cdot 1+1^{2} } =\\\\\\=\sqrt{(2\sqrt{2} -1)^{2} } =\Big|2\sqrt{2} -1\Big|=2\sqrt{2} -1\\\\2)\\\\\sqrt{17-12\sqrt{2} } =\sqrt{8-12\sqrt{2} +9} =\sqrt{(2\sqrt{2} )^{2} -2\cdot 2\sqrt{2}\cdot 3+3^{2} } =\\\\\\=\sqrt{(2\sqrt{2} -3)^{2} } =\Big|2\sqrt{2} -3\Big|=3-2\sqrt{2}$