Question

Rút gọn 

a, \(\dfrac{\sqrt{2}-2}{1-\sqrt{2}}\)

b, \(\dfrac{1}{\sqrt{3}+2}\)

c, \(\dfrac{5}{2-\sqrt{7}}\)

d, \(\dfrac{9}{2\sqrt{3}}\)

Answer 1

\(\dfrac{\sqrt{2}-2}{1-\sqrt{2}}=\dfrac{\sqrt{2}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}=\sqrt{2}\)

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

\(\dfrac{9}{2\sqrt{3}}=\dfrac{9\sqrt{3}}{2\sqrt{3}^2}=\dfrac{9\sqrt{3}}{2.3}=\dfrac{3\sqrt{3}}{2}\)

\(\dfrac{5}{2-\sqrt{7}}=\dfrac{5\left(2+\sqrt{7}\right)}{\left(2-\sqrt{7}\right)\left(2+\sqrt{7}\right)}=\dfrac{5\left(2+\sqrt{7}\right)}{2^2-\sqrt{7}^2}=\dfrac{5\left(2+\sqrt{7}\right)}{4-7}=-\dfrac{5\left(2+\sqrt{7}\right)}{3}\)