Question

Rút gọn các biểu thức sau :

a) \(\sqrt{18}-\) \(2\sqrt{50}+\sqrt{\left(2-\sqrt{2}\right)^2}\)

b) \(\sqrt{\dfrac{1}{3}}+\dfrac{3}{\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}\)

c) \(\left(1+\sqrt{2}+\sqrt{3}\right)\)\(\left(1+\sqrt{2}-\sqrt{3}\right)\)

d) \(3\sqrt{200}-\)\(2\sqrt{0,08}-\)\(4\sqrt{\dfrac{9}{8}}\)

Answer 1

a) \(\sqrt{18}\)-2\(\sqrt{50}\)+\(\sqrt{\left(2-\sqrt{2}\right)^2}\)

=3\(\sqrt{2}\)-10\(\sqrt{2}\)+(2-\(\sqrt{2}\))²

= 3\(\sqrt{2}\)-10\(\sqrt{2}\)+4-2

= -7\(\sqrt{2}\)+2

Answer 2

a) \(\sqrt{18}-2\sqrt{50}+\sqrt{\left(2-\sqrt{2}\right)^2}\)

=\(3\sqrt{2}-10\sqrt{2}+2-\sqrt{2}=2-8\sqrt{2}\)

b)\(\sqrt{\dfrac{1}{3}}+\dfrac{3}{\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}\)

=\(\dfrac{1}{3}\sqrt{3}+\sqrt{3}+\dfrac{1}{2-\sqrt{3}}=\dfrac{4}{3}\sqrt{3}+\dfrac{1}{2-\sqrt{3}}\)

=\(\dfrac{4\sqrt{3}+2+\sqrt{3}}{3}=\dfrac{5\sqrt{3}+2}{3}\)

c)\(\left(1+\sqrt{2}+\sqrt{3}\right)\left(1+\sqrt{2}-\sqrt{3}\right)\)

=\(\left(1+\sqrt{2}\right)^2-3=1+2\sqrt{2}+2-3=2\sqrt{2}\)

d)\(3\sqrt{200}-2\sqrt{0,08}-4\sqrt{\dfrac{9}{8}}\)

=\(30\sqrt{2}-0,4\sqrt{2}-3\sqrt{2}=26.6\sqrt{2}\)