Đáp án:

Giải thích các bước giải:

Bài làm :

a, `\sqrt{8+2\sqrt{7}}-\sqrt{8-2\sqrt{7}}`

`=\sqrt{7+2.\sqrt{7}.1+1}-\sqrt{7-2.\sqrt{7}.1+1}`

`=\sqrt{(\sqrt{7})^2+2.\sqrt{7}.1+1^2}-\sqrt{(\sqrt{7})^2-2.\sqrt{7}.1+1^2}`

`=\sqrt{(\sqrt{7}+1)^2}-\sqrt{(\sqrt{7}-1)^2}`

`=|\sqrt{7}+1|-|\sqrt{7}-1|`

`=\sqrt{7}+1-(\sqrt{7}-1)`

`=\sqrt{7}+1-\sqrt{7}+1`

`=2`

b, `\sqrt{13+4\sqrt{3}}+\sqrt{4-2\sqrt{3}}-3\sqrt{3}`

`=\sqrt{12+2.2\sqrt{3}.1+1}+\sqrt{3-2\sqrt{3}.1+1}-3\sqrt{3}`

`=\sqrt{(2\sqrt{3})^2+2.2\sqrt{3}.1+1^2}+\sqrt{(\sqrt{3})^2-2\sqrt{3}.1+1^2}-3\sqrt{3}`

`=\sqrt{(2\sqrt{3}+1)^2}+\sqrt{(\sqrt{3}-1)^2}-3\sqrt{3}`

`=|2\sqrt{3}+1|+|\sqrt{3}-1|-3\sqrt{3}`

`=2\sqrt{3}+1+\sqrt{3}-1-3\sqrt{3}`

`=0`

c, Đặt `A=\sqrt{8-\sqrt{15}}-\sqrt{8+\sqrt{15}}`

`=>\sqrt{2}.A=\sqrt{2}.\sqrt{8-\sqrt{15}}-\sqrt{2}.\sqrt{8+\sqrt{15}}`

`=>\sqrt{2}.A=\sqrt{16-2\sqrt{15}}-\sqrt{16+2\sqrt{15}}`

`=>\sqrt{2}.A=\sqrt{15-2\sqrt{15}.1+1}-\sqrt{15+2\sqrt{15}.1+1}`

`=>\sqrt{2}.A=\sqrt{(\sqrt{15})^2-2\sqrt{15}.1+1^2}-\sqrt{(\sqrt{15})^2+2\sqrt{15}.1+1^2}`

`=>\sqrt{2}.A=\sqrt{(\sqrt{15}-1)^2}-\sqrt{(\sqrt{15}+1)^2}`

`=>\sqrt{2}.A=|\sqrt{15}-1|-|\sqrt{15}+1|`

`=>\sqrt{2}.A=\sqrt{15}-1-(\sqrt{15}+1)`

`=>\sqrt{2}.A=\sqrt{15}-1-\sqrt{15}-1`

`=>\sqrt{2}.A=-2`

`=>A=-\sqrt{2}`

d, `\sqrt{a^2}-3a`

`=|a|-3a`

`=a-3a` ( vì `a>0` )

`=-2a`

e, `2x-2+\sqrt{4x^2-4x+1}`

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

`=2x-2+|2x-1|`

`=2x-2+2x-1` ( vì `x>1` )

`=4x-3`

f, `\sqrt{4x^2-4x+1}+2x`

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

`=|2x-1|+2x`

`=-(2x-1)+2x` ( vì `x<0,5` )

`=-2x+1+2x`

`=1`