a, $\frac{\sqrt{6+2√5}}{√5+1}$ 

=$\frac{\sqrt{5+2√5+1}}{√5+1}$ 

=$\frac{\sqrt{(√5+1)^2}}{√5+1}$ 

=$\frac{√5+1}{√5+1}$ =1

b, $\frac{\sqrt{7-4√3}}{√3-2}$ 

= $\frac{\sqrt{4-4√3+3}}{√3-2}$ 

=$\frac{\sqrt{(2-√3)^2}}{√3-2}$ 

=$\frac{2-√3}{√3-2}$ =-1 

c,$\frac{\sqrt{5-2√6}}{√10 -√15}$

= $\frac{\sqrt{2-2√6+3}}{√ 5(√ 2-√ 3)}$

=$\frac{\sqrt{(√ 2-√ 3)^2}}{√ 5(√ 3-√ 2)}$

=$\frac{√ 2 − √ 3}{√ 5(√ 3-√ 2)}$

=$\frac{-1}{√5}$ 

d,$\frac{5-√5}{\sqrt{6-2√5}}$

=$\frac{√5(√5-1)}{\sqrt{5-2√5+1}}$

=$\frac{√5(√5-1)}{\sqrt{(√5-1)^2}}$ 

=$\frac{√5(√5-1)}{ √ 5 − 1 }$ 

=√5

Chúc bạn học tốt !!

Đáp án:

Giải thích các bước giải:

 Bài `4`

`a)`

`(\sqrt{6+2\sqrt{5}})/(\sqrt{5}+1)`

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

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

`=(\sqrt{5}+1)/(\sqrt{5}+1)`

`=1`

`b)`

`(\sqrt{7-4\sqrt{3}})/(\sqrt{3}-2)`

`=(\sqrt{4-4\sqrt{5}+3})/(\sqrt{3}-2)`

`=\sqrt{(2-\sqrt{3})^2)/(\sqrt{3}-2)`

`=(2-\sqrt{3})/(\sqrt{3}-2)`

`=-1`

`c)`

`(\sqrt{5-2\sqrt{6}})/(\sqrt{10}-\sqrt{15})`

`=[\sqrt{2}.(\sqrt{5-2\sqrt{6}})]/(\sqrt{2}.(\sqrt{10}-\sqrt{15})`

`=(\sqrt{10-4\sqrt{6}})/(\sqrt{20}-\sqrt{30})`

`=(\sqrt{6-4\sqrt{6}+4})/(\sqrt{20}-\sqrt{30})`

`=(\sqrt{(\sqrt{6}-2)^2})/(\sqrt{20}-\sqrt{30})`

`=(\sqrt{(\sqrt{6}-2)^2})/(\sqrt{20}-\sqrt{30})`

`=(\sqrt{6}-2)/(\sqrt{20}-\sqrt{30})`

`=-(\sqrt{6}-2)/(\sqrt{30}-\sqrt{20})`

`=-(\sqrt{6}-2)/(\sqrt{5}.(\sqrt{6}-2)`

`=-1/(\sqrt{5}`

`d)`

`(5-\sqrt{5})/(\sqrt{6-2\sqrt{5}})`

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

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

`=(5-\sqrt{5})/(\sqrt{5}-1)`

`=(\sqrt{5}(\sqrt{5}-1))/(\sqrt{5}-1)`

`=\sqrt{5}`