Đáp án:
`b)` ` 4\sqrt{5}+3\sqrt{3}`
`c)` `\sqrt{x-4}+2` với `x\ge 4`
`d)` `\sqrt{6}`
Giải thích các bước giải:
`5b)` `\sqrt{8+\sqrt{60}}+\sqrt{45}+\sqrt{12}`
`=\sqrt{8+\sqrt{2^2 . 15}}+\sqrt{3^2 .5}+\sqrt{2^2 . 3}`
`=\sqrt{8+2\sqrt{15}}+3\sqrt{5}+2\sqrt{3}`
`=\sqrt{5+2\sqrt{5}.\sqrt{3}+3}+3\sqrt{5}+2\sqrt{3}`
`=\sqrt{(\sqrt{5}+\sqrt{3})^2}+3\sqrt{5}+2\sqrt{3}`
`=\sqrt{5}+\sqrt{3}+3\sqrt{5}+2\sqrt{3}`
`=4\sqrt{5}+3\sqrt{3}`
$\\$
`c)` `\sqrt{x+4\sqrt{x-4}}``\quad (x\ge 4)`
`=\sqrt{x-4+2.\sqrt{x-4}.2+2^2}`
`=\sqrt{(\sqrt{x-4}+2)^2}`
`=|\sqrt{x-4}+2|=\sqrt{x-4}+2`
$\\$
`d)` `\sqrt{5}+\sqrt{11-2\sqrt{30}}`
`=\sqrt{5}+\sqrt{6-2\sqrt{6}.\sqrt{5}+5}`
`=\sqrt{5}+\sqrt{(\sqrt{6}-\sqrt{5})^2}`
`=\sqrt{5}+|\sqrt{6}-\sqrt{5}|`
`=\sqrt{5}+\sqrt{6}-\sqrt{5}=\sqrt{6}`
