BÀI 1 trục căn thức ở mẫu:
1) \(\dfrac{2\sqrt{5}-\sqrt{15}}{\sqrt{5}}\)
2) \(\dfrac{\sqrt{2}-\sqrt{8}}{6\sqrt{2}}\)
3) \(\dfrac{5+3\sqrt{5}}{3+\sqrt{5}}\)
4) \(\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\)
5) \(\dfrac{\sqrt{2}-\sqrt{6}}{3\sqrt{3}-3}\)
BÀI 2:Rút gọn
1) \(\dfrac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}-\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)
2) \(\dfrac{3+\sqrt{3}}{\sqrt{3}}+\dfrac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}\)
3) \(\dfrac{2}{\sqrt{3}-1}-\dfrac{2}{\sqrt{3}+1}\)
4) \(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}\)
5) \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}\)
6) \(\dfrac{4}{3+\sqrt{5}}-\dfrac{8}{1+\sqrt{5}}+\dfrac{15}{\sqrt{5}}\)
Bài 1:
1: \(=\dfrac{\sqrt{5}\left(2-\sqrt{3}\right)}{\sqrt{5}}=2-\sqrt{3}\)
2: \(=\dfrac{-\sqrt{2}}{6\sqrt{2}}=\dfrac{-1}{6}\)
3: \(=\dfrac{\sqrt{5}\left(3+\sqrt{5}\right)}{3+\sqrt{5}}=\sqrt{5}\)
4: \(=\dfrac{-\sqrt{5}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}=-\sqrt{5}\)
\(a,=\dfrac{\sqrt{5}\left(2-\sqrt{3}\right)}{\sqrt{5}}\\ =2-\sqrt{3}\\ b,=\dfrac{\sqrt{2}\left(1-\sqrt{4}\right)}{6\sqrt{2}}\\ =\dfrac{1-\sqrt{4}}{6}=-\dfrac{1}{6}\\ c,\\=\dfrac{\sqrt{5}\left(\sqrt{5}+3\right)}{3+\sqrt{5}}\\ =\sqrt{5}\\ d,=\dfrac{-\sqrt{5}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}\\ =-\sqrt{5}\\ e,=\dfrac{\sqrt{2}\left(1-\sqrt{3}\right)}{-3\left(1-\sqrt{3}\right)}\\ =\dfrac{-\sqrt{2}}{3}\)
