\(a,\left(\sqrt{27}-2\sqrt{17}+\sqrt{7}\right)\cdot\sqrt{7}+7\sqrt{8}\)
\(=3\sqrt{21}-2\sqrt{119}+7+7\sqrt{8}\)
Đề sai chăng???
\(b,\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}\)
\(=\sqrt{2-2\sqrt{2}+1}+\sqrt{2+2\sqrt{2}+1}\)
\(=\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(\sqrt{2}+1\right)^2}\)
\(=\sqrt{2}-1+\sqrt{2}+1\)
\(=2\sqrt{2}\)
\(c,9\sqrt{2}-4\sqrt{8}-\sqrt{50}+2\sqrt{32}\)
\(=9\sqrt{2}-8\sqrt{2}-5\sqrt{2}+8\sqrt{2}\)
\(=\sqrt{2}\left(9-8-5+8\right)\)
\(=4\sqrt{2}\)
\(d,\sqrt{3-2\sqrt{2}}-\sqrt{6+4\sqrt{2}}\)
\(=\sqrt{2-2\sqrt{2}+1}-\sqrt{4+2.2\sqrt{2}+2}\)
\(=\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{\left(2+\sqrt{2}\right)^2}\)
\(=\sqrt{2}-1-2-\sqrt{2}\)
\(=-3\)
\(c,9\sqrt{2}-4\sqrt{8}-\sqrt{50}+2\sqrt{32}\)
\(=9\sqrt{2}-8\sqrt{2}-5\sqrt{2}+8\sqrt{2}\)
\(=4\sqrt{2}\)
a) \(\left(\sqrt{27}-2\sqrt{17}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
\(=\sqrt{7}.\left(3\sqrt{3}+\sqrt{7}-2\sqrt{17}\right)+14\sqrt{2}\)
\(=3\sqrt{21}-2\sqrt{119}+7+14\sqrt{2}\)
b) \(\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}\)
\(=\sqrt{2}-1+\sqrt{2}+1\)
\(=2\sqrt{2}-1+1\)
\(=2\sqrt{2}\)
c) \(9\sqrt{2}-4\sqrt{8}-\sqrt{50}+2\sqrt{32}\)
\(=9\sqrt{2}-8\sqrt{2}-5\sqrt{2}+8\sqrt{2}\)
\(=9\sqrt{2}-5\sqrt{2}\)
\(=4\sqrt{2}\)
d) \(\sqrt{3-2\sqrt{2}}-\sqrt{6+4\sqrt{2}}\)
\(=\sqrt{2}-1-\left(2+\sqrt{2}\right)\)
\(=\sqrt{2}-1-\sqrt{2}-2\)
= -1 - 2
= -3
