Question

√(8-6√8+9) +2√2 как решить?подробно

Answer 1

$\sqrt{(8 - 6 \sqrt{8} + 9) } + 2 \sqrt{2}$

$\sqrt{( \sqrt{8} - 3)^{2} } + 2 \sqrt{2}$

$3 - \sqrt{8} + 2 \sqrt{2}$

$3 - 2 \sqrt{2} + 2 \sqrt{2}$

$3$

Answer 2

$\tt{} \ \ \ \sqrt{8-6\sqrt{8}+9}+2\sqrt{2}= \sqrt{(\sqrt{8})^2-2\cdot\sqrt{8}\cdot3+3^2}+2\sqrt{2} =\\\\=\sqrt{(\sqrt{8}-3)^2}+2\sqrt{2} =|\sqrt{8}-3|+2\sqrt{2}=3-\sqrt{8}+2\sqrt{2}=\\\\=3-2\sqrt{2}+2\sqrt{2}=3$