Question

1)Rút gonj biểu thức 

a)\(\dfrac{1}{\sqrt{2}-1}\)             b)\(\sqrt{4+2\sqrt{3}}\)            c)\(\sqrt{5-2\sqrt{6}}\)             d)\(\dfrac{\sqrt{15}-\sqrt{6}}{\sqrt{2}-\sqrt{5}}\)

e)\(\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)

Answer 1

`a)1/[\sqrt{2}-1]=[\sqrt{2}+1]/[2-1]=\sqrt{2}+1`

`b)\sqrt{4+2\sqrt{3}}=\sqrt{3+2\sqrt{3}+1}=\sqrt{(\sqrt{3}+1)^2}=|\sqrt{3}+1|=\sqrt{3}+1`

`c)\sqrt{5-2\sqrt{6}}=\sqrt{3-2\sqrt{3}.\sqrt{2}+2}=\sqrt{(\sqrt{3}-\sqrt{2})^2}=|\sqrt{3}-\sqrt{2}|=\sqrt{3}-\sqrt{2}`

`d)[\sqrt{15}-\sqrt{6}]/[\sqrt{2}-\sqrt{5}]=[-\sqrt{3}(\sqrt{2}-\sqrt{5})]/[\sqrt{2}-\sqrt{5}]=-\sqrt{3}`

`e)\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}`

`=\sqrt{5-2\sqrt{5}+1}+\sqrt{5+2\sqrt{5}+1}`

`=\sqrt{(\sqrt{5}-1)^2}+\sqrt{(\sqrt{5}+1)^2}`

`=|\sqrt{5}-1|+|\sqrt{5}+1|`

`=\sqrt{5}-1+\sqrt{5}+1=2\sqrt{5}`