Question

Thực hiện phép tính:

a. \(2\sqrt{2}-3\sqrt{18}+4\sqrt{32}-2\sqrt{50}\)

b. \(\sqrt{6+2\sqrt{5}}+\sqrt{\left(\sqrt{5}-7\right)^2}\)

c. \(\dfrac{1}{2-\sqrt{6}}-\dfrac{1}{2+\sqrt{6}}\)

Answer 1

\(a.2\sqrt{2}-3\sqrt{18}+4\sqrt{32}-2\sqrt{50}=2\sqrt{2}-9\sqrt{2}+16\sqrt{2}-10\sqrt{2}=-\sqrt{2}\)

\(b.\sqrt{6+2\sqrt{5}}+\sqrt{\left(\sqrt{5}-7\right)^2}=\sqrt{5+2\sqrt{2}+1}+\sqrt{\left(\sqrt{5}-7\right)^2}=\sqrt{5}+1+7-\sqrt{5}=8\)

\(c.\dfrac{1}{2-\sqrt{6}}-\dfrac{1}{2+\sqrt{6}}=\dfrac{2+\sqrt{6}-2+\sqrt{6}}{\left(2-\sqrt{6}\right)\left(2+\sqrt{6}\right)}=\dfrac{2\sqrt{6}}{-2}=-\sqrt{6}\)