Đáp án + Giải thích các bước giải:
a)
`\sqrt{2+\sqrt3}+\sqrt{2-\sqrt3}`
`=(\sqrt2(\sqrt{2+\sqrt3}+\sqrt{2-\sqrt3}))/(\sqrt2)`
`=(\sqrt{2(2+\sqrt3)}+\sqrt{2(2-\sqrt3)})/(\sqrt2)`
`=(\sqrt{4+2\sqrt3}+\sqrt{4-2\sqrt3})/(\sqrt2)`
`=(\sqrt{3+2\sqrt3+1}+\sqrt{3-2\sqrt3+1})/(\sqrt2)`
`=(\sqrt{(\sqrt3+1)^2}+\sqrt{(\sqrt3-1)^2})/(\sqrt2)`
`=(|\sqrt3+1|+|\sqrt3-1|)/(\sqrt2)`
`=(\sqrt3+1+\sqrt3-1)/(\sqrt2)`
`=(2\sqrt3)/(\sqrt2)`
`=\sqrt2.\sqrt3`
`=\sqrt6`
Vậy `\sqrt{2+\sqrt3}+\sqrt{2-\sqrt3}=\sqrt6`
b)
`\sqrt{4/(2-\sqrt5)^2}-\sqrt{4/(2+\sqrt5)^2}`
`=\sqrt{(2/(2-\sqrt5))^2}-\sqrt{(2/(2+\sqrt5))^2}`
`=|2/(2-\sqrt5)|-|2/(2+\sqrt5|`
`=2/(\sqrt5-2)-2/(\sqrt5+2)`
`=(2(\sqrt5+2))/(5-4)-(2(\sqrt5-2))/(5-4)`
`=2\sqrt5+4-2\sqrt5+4`
`=8`
Vậy `\sqrt{4/(2-\sqrt5)^2}-\sqrt{4/(2+\sqrt5)^2}=8`
