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a, \(\sqrt{2}A=\sqrt{10-2\sqrt{3.7}}+\sqrt{10+2\sqrt{3.7}}\)
\(=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{3}+\sqrt{7}\right)^2}\)
\(=\left|\sqrt{7}-\sqrt{3}\right|+\left|\sqrt{7}+\sqrt{3}\right|\)
\(=\sqrt{7}-\sqrt{3}+\sqrt{3}+\sqrt{7}=2\sqrt{7}\)
\(\Rightarrow A=\sqrt{14}\)
b, \(B=\frac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}+\frac{\sqrt{5}\left(\sqrt{5}-2\right)}{2\left(\sqrt{5}-2\right)}\)
\(=\sqrt{5}+\frac{\sqrt{5}}{2}=\frac{3\sqrt{5}}{2}\)
c, \(C=\left(1-\sqrt{11}\right)\left(\sqrt{11}+1\right)=1-11=-10\)
d, \(D=\frac{\sqrt{2}\left(\sqrt{2}+\sqrt{3}\right)}{2-3}-\frac{\sqrt{2}\left(\sqrt{2}-\sqrt{3}\right)}{2-3}\)
\(=-2-\sqrt{6}+2-\sqrt{6}=-2\sqrt{6}\)
a: \(=6-\sqrt{15}+2\sqrt{15}=6+\sqrt{15}\)
b: \(=\left(\sqrt{7}-2\sqrt{3}\right)\cdot\sqrt{7}+2\sqrt{21}\)
\(=7-2\sqrt{21}+2\sqrt{21}=7\)
c: \(=10+5\sqrt{10}-5\sqrt{10}=10\)
d: \(=22-\sqrt{198}+\sqrt{198}=22\)
trinh mai
\(\sqrt{\left(\sqrt{2}-3\right)^2}.\sqrt{3^2+3.2\sqrt{2}+2}=\sqrt{\left(3-\sqrt{2}\right)^2}.\sqrt{\left(3+\sqrt{2}\right)^2}=\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)=3^2-2=7\)
\(a,\sqrt{17-4\sqrt{9+4\sqrt{5}}}=\sqrt{17-4\sqrt{5+4\sqrt{5}+4}}=\sqrt{17-4\sqrt{\left(\sqrt{5}\right)^2+2.2\sqrt{5}+2^2}}=\sqrt{17-4\sqrt{\sqrt{\left(\sqrt{5}+2\right)^2}}}=\sqrt{17-4\sqrt{\sqrt{5}+2}}\) \(b,\sqrt{a};đk:a\ge0;2-3=-1< 0\Rightarrow sai\)
\(c,\sqrt{\left(\sqrt{3-3}\right)^2}.\sqrt{\frac{1}{3-\sqrt{3}}}=\sqrt{0^2}.\sqrt{\frac{1}{3-\sqrt{3}}}=0.\sqrt{\frac{1}{3-\sqrt{3}}}=0\)
\(d,\left(\sqrt{6}-3\sqrt{3}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right)2\sqrt{6}=\left(\sqrt{2}.\sqrt{3}-3\sqrt{3}+5\sqrt{2}-\sqrt{2}\right)2\sqrt{6}=\left[\sqrt{3}\left(\sqrt{2}-3\right)+\sqrt{2}.4\right]2\sqrt{6}=\left[2.\sqrt{3}.\sqrt{2}.\sqrt{3}\left(\sqrt{2}-3\right)+\sqrt{2}.\sqrt{2}.\sqrt{3}.2.4\right]=6\sqrt{2}\left(\sqrt{2}-3\right)+16\sqrt{3}\)
a) \(\left(2\sqrt{3}+\sqrt{5}\right)\sqrt{3}-\sqrt{60}\) = \(6+\sqrt{15}-2\sqrt{15}\)
= \(6-\sqrt{15}\)
b) \(\left(5\sqrt{2}+2\sqrt{5}\right)\sqrt{5}-\sqrt{250}\) = \(5\sqrt{10}+10-5\sqrt{10}\) = \(10\)
c) \(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\) = \(14-2\sqrt{21}-7+2\sqrt{21}\)
= \(7\)
d) \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)
= \(33-3\sqrt{22}-11+3\sqrt{22}\) = \(22\)
a)(2√3+√5)√3-√60
=6+√15-2√15
=6-√15
b)(5√2+2√5)√5-√250
=5√10+10-5√10
=10
c)(√28-√12-√7)√7+2√21
=14-2√21-7+2√21
=7
d)(√99-√18-√11)√11+3√22
=33-3√22-11+3√22
=22
\(B=\left|5+3\sqrt{2}\right|+\left|\sqrt{11}-3\sqrt{2}\right|+\frac{11}{\sqrt{11}}\)
\(=5+3\sqrt{2} +3\sqrt{2}-\sqrt{11}+\sqrt{11}\)
\(=5+6\sqrt{2}\)