Rút gọn biểu thức
a) \(\sqrt{\left(1+2\sqrt{3}\right)^2}-5\sqrt{3}\)
= \(\left|1+2\sqrt{3}\right|-5\sqrt{3}\)
= \(1+2\sqrt{3}-5\sqrt{3}=1-3\sqrt{3}\)
b) \(3\sqrt{2}+4\sqrt{8}-\sqrt{18}\)
= \(3\sqrt{2}+4\sqrt{2.4}-\sqrt{2.9}\)
= \(3\sqrt{2}+8\sqrt{2}-3\sqrt{2}\) = \(8\sqrt{2}\)
a)\(\sqrt{\left(1+2\sqrt{3}\right)^2}-5\sqrt{3}=1+2\sqrt{3}-5\sqrt{3}=1-3\sqrt{3}\)
b)\(3\sqrt{2}-4\sqrt{8}-\sqrt{18}=3\sqrt{2}-8\sqrt{2}-3\sqrt{2}=-8\sqrt{2}\)
c)\(\dfrac{1}{3+\sqrt{2}}+\dfrac{1}{3-\sqrt{2}}=\dfrac{3-\sqrt{2}+3+\sqrt{2}}{\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)}=\dfrac{6}{5}\)
c) \(\dfrac{1}{3+\sqrt{2}}+\dfrac{1}{3-\sqrt{2}}=\dfrac{3+\sqrt{2}+3-\sqrt{2}}{\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)}=\dfrac{6}{\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)}\)
