1.Thực hiện phép tính:
a) (\(\sqrt{72}\)-3\(\sqrt{5}\)+2\(\sqrt{8}\)).\(\sqrt{2}\)+\(\sqrt{90}\)
b) (\(\sqrt{\dfrac{1}{5}}\)-10.\(\sqrt{\dfrac{27}{5}}\)+2\(\sqrt{5}\)):\(\sqrt{5}\)+6\(\sqrt{3}\)
2. Rút gọn các biểu thức sau:
a)\(\sqrt{\left(3-\sqrt{10}\right)^{ }2}\)
b) \(\sqrt{7+4\sqrt{3}}\)+ \(\sqrt{7-4\sqrt{3}}\)
c) \(\dfrac{2+\sqrt{2}}{1+\sqrt{2}}\)
\(1a.\left(\sqrt{72}-3\sqrt{5}+2\sqrt{8}\right).\sqrt{2}+\sqrt{90}=\sqrt{144}-3\sqrt{10}+2.\sqrt{16}+3\sqrt{10}=12+8=20\) \(b.\left(\sqrt{\dfrac{1}{5}}-10\sqrt{\dfrac{27}{5}}+2\sqrt{5}\right):\sqrt{5}+6\sqrt{3}=\left(\sqrt{\dfrac{1}{5}}-30\sqrt{\dfrac{3}{5}}+2\sqrt{5}\right).\dfrac{1}{\sqrt{5}}+6\sqrt{3}=\dfrac{1}{5}-6\sqrt{3}+2+6\sqrt{3}=\dfrac{11}{5}\) \(2.\sqrt{\left(3-\sqrt{10}\right)^2}=\sqrt{10}-3\)
\(b.\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}=\sqrt{4+2.2\sqrt{3}+3}+\sqrt{4-2.2.\sqrt{3}+3}=2+\sqrt{3}+2-\sqrt{3}=4\) \(c.\dfrac{2+\sqrt{2}}{1+\sqrt{2}}=\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{1+\sqrt{2}}=\sqrt{2}\)
