Question

Rút gọn các biểu thức:
a) \(\left(5\sqrt{2}+2\sqrt{5}\right).\sqrt{5}-\sqrt{250}\)
b) \(\dfrac{2\sqrt{3}}{\sqrt{6}-2}-\dfrac{2\sqrt{3}}{\sqrt{6}+2}\)
-GIÚP MÌNH VỚI Ạ-

Answer 1

a)\(\left(5\sqrt{2}+2\sqrt{5}\right)\cdot\sqrt{5}-\sqrt{250}\)

\(=5\sqrt{10}+10-5\sqrt{10}\\ =10\)

b)\(\dfrac{2\sqrt{3}}{\sqrt{6}-2}-\dfrac{2\sqrt{3}}{\sqrt{6}+2}\)

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

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

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

\(4\sqrt{3}\)