1 rút gọn A= $\sqrt{3-2\sqrt{2}}$ - $\sqrt{6-4\sqrt{2}}$

Đáp án:

`A=2sqrt{2}-3`

Giải thích các bước giải:

`A=sqrt{3-2sqrt{2}}-sqrt{6-4sqrt{2}}`
`A=sqrt{(sqrt{2})^2-2.sqrt{2}.1+1^2}-sqrt{6-2.2sqrt{2}}`
`A=sqrt{(sqrt{2}-1)^2}-sqrt{2^2-2.2.sqrt{2}+(sqrt{2})^2}`
`A=sqrt{(sqrt{2}-1)^2}-sqrt{(2-sqrt{2})^2}`
`A=|sqrt{2}-1|-|2-sqrt{2}|`
`A=sqrt{2}-1-2+sqrt{2}`
`A=2sqrt{2}-3`
Giải thích:
`|sqrt{2}-1|=sqrt{2}-1` vì `sqrt{2}>sqrt{1}=1`
`|2-sqrt{2}|=2-sqrt{2}` vì `sqrt{4}(=2)>sqrt{2}`

`A` `=` `\sqrt{3-\sqrt{2}}` `-` `\sqrt{6-4\sqrt{2}}`

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

`=` `|\sqrt{2}-1|` `-` `|2-\sqrt{2}|`

`=` `\sqrt{2}` `-` `1` `-` `(2-\sqrt{2})`

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

`=` `2\sqrt{2}` `-` `3`