a) \(=\left|2\sqrt{6}+5\right|-\left|2\sqrt{6}-5\right|=2\sqrt{6}+5+2\sqrt{6}-5=4\sqrt{6}\)
b) \(=5\sqrt{2}-\left(\sqrt{8}-\sqrt{3}\right)-\sqrt{3}=5\sqrt{2}-\sqrt{8}+\sqrt{3}-\sqrt{3}=5\sqrt{2}-\sqrt{8}\)
c) \(=\sqrt{\left(\sqrt{7}-1\right)^2}+\sqrt{\left(\sqrt{7}+1\right)^2}=\sqrt{7}-1+\sqrt{7}+1=2\sqrt{7}\)
d) \(=\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{\left(2-\sqrt{3}\right)^2}=2+\sqrt{3}-2+\sqrt{3}=2\sqrt{3}\)
e) \(=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}=-2\sqrt{3}\)
f) \(=\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(3-2\sqrt{2}\right)^2}-3\sqrt{2}=3-\sqrt{2}-3+2\sqrt{2}-3\sqrt{2}=-2\sqrt{2}\)
h) \(2+\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
\(=2+\sqrt{17-4\sqrt{\left(2+\sqrt{5}\right)^2}}\)
\(=2+\sqrt{17-4\left|2+\sqrt{5}\right|}\)
\(=2+\sqrt{9-4\sqrt{5}}\)
\(=2+\sqrt{\left(2-\sqrt{5}\right)^2}=2+\left|2-\sqrt{5}\right|=2+\sqrt{5}-2=\sqrt{5}\)
i) \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
\(=\sqrt{13+30\sqrt{2+\sqrt{\left(1+2\sqrt{2}\right)^2}}}\)
\(=\sqrt{13+30\sqrt{3+2\sqrt{2}}}=\sqrt{13+30\sqrt{\left(1+\sqrt{2}\right)^2}}=\sqrt{43+30\sqrt{2}}\)
\(=\sqrt{25+30\sqrt{2}+18}=\sqrt{\left(5+3\sqrt{2}\right)^2}=5+3\sqrt{2}\)
Các cao nhân giúp em bài màu hồng hồng với ạ, em bị ngáo tạm thời. Mong giúp em chứ em làm nãy h kh ra ạ
