Question

6) Thực hiện các phép tính
a. \(\sqrt{2}\left(\sqrt{8}+\sqrt{32}-\sqrt{98}\right)\)
b. \(\dfrac{2}{\sqrt{5}+2}+\dfrac{2}{2-\sqrt{5}}\)
c. \(\left(2+\sqrt{3}\right)\sqrt{11-6\sqrt{2}}\)
 Mng giúp mik vs ạ >.<!!

Answer 1

b, \(\dfrac{2}{\sqrt{5}+2}+\dfrac{2}{2-\sqrt{5}}\)

\(=\dfrac{2\left(\sqrt{5}-2\right)}{5-4}-\dfrac{2\left(\sqrt{5}+2\right)}{5-4}\)

\(=2\sqrt{5}-4-2\sqrt{5}-4=-8\)

Answer 2

a, \(\sqrt{2}\left(\sqrt{8}+\sqrt{32}-\sqrt{98}\right)\)

\(=\sqrt{2}\left(2\sqrt{2}+4\sqrt{2}-7\sqrt{2}\right)\)

\(=\sqrt{2}.\left(-\sqrt{2}\right)=-2\)

Answer 3

c, \(\left(2+\sqrt{3}\right)\sqrt{11-6\sqrt{2}}\)

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

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

\(=6-2\sqrt{2}+3\sqrt{3}-\sqrt{6}\)

Answer 4

a: Ta có: \(\sqrt{2}\left(\sqrt{8}+\sqrt{32}-\sqrt{98}\right)\)

\(=\sqrt{2}\left(2\sqrt{2}+4\sqrt{2}-7\sqrt{2}\right)\)

=-2

b: Ta có: \(\dfrac{2}{\sqrt{5}+2}-\dfrac{2}{\sqrt{5}-2}\)

\(=2\sqrt{5}-4-2\sqrt{5}-4\)

=-8

c: Ta có: \(\left(2+\sqrt{3}\right)\cdot\sqrt{11-6\sqrt{2}}\)

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

\(=6-2\sqrt{2}+3\sqrt{3}-\sqrt{6}\)

Answer 5

àdsadf