Question

rút gọn biểu thức

a) \(3\sqrt{8}-4\sqrt{18}+5\sqrt{32}-\sqrt{50}\)

b) (\(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\)) : 10

c) \(2\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}\)

d) (\(\sqrt{14}-3\sqrt{2}\))\(^2\) +\(6\sqrt{28}\)

e) \(\sqrt{\left(1-\sqrt{2018}\right)^2}\). \(\sqrt{2019+2\sqrt{2018}}\)

f) \(\left(\sqrt{6}-\sqrt{5}\right)^2-\sqrt{120}\)

g)\(12\left(2\sqrt{3}-3\sqrt{2}\right)^2+2\sqrt{6}+3\sqrt{4}\)

Answer 1

a) \(3\sqrt{8}-4\sqrt{18}+5\sqrt{32}-\sqrt{50}=3\sqrt{4.2}-4\sqrt{9.2}+5\sqrt{16.2}-\sqrt{25.2}=6\sqrt{2}-12\sqrt{2}+20\sqrt{2}-5\sqrt{2}=9\sqrt{2}\)b) \(\left(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\right):10=\left(15\sqrt{50}+5\sqrt{50.4}-3\sqrt{50.9}\right):10=\left(15\sqrt{50}+10\sqrt{50}-9\sqrt{50}\right):10=\dfrac{16\sqrt{50}}{10}=\dfrac{16\sqrt{25.2}}{10}=\dfrac{80\sqrt{2}}{10}=8\sqrt{2}\) c) \(2\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}=2\sqrt{7.4}+2\sqrt{7.9}-3\sqrt{7.25}+\sqrt{7.16}=4\sqrt{7}+6\sqrt{7}-15\sqrt{7}+4\sqrt{7}=-\sqrt{7}\)

d)
\(\left(\sqrt{14}-3\sqrt{2}\right)^2+6\sqrt{28}=14-2.3\sqrt{2.14}+18+6\sqrt{28}=32-6\sqrt{28}+6\sqrt{28}=32\)