B5:
a) `9+4\sqrt5=(\sqrt5+2)^2`
VT: `9+4\sqrt5`
`=(\sqrt5)^2+2.2\sqrt5+2^2`
`=(\sqrt5+2)^2`
Vậy: `9+4\sqrt5=(\sqrt5+2)^2` (đpcm)
b) `(4-\sqrt7)^2=23-8\sqrt7`
VT: `(4-\sqrt7)^2`
`=16-2.4\sqrt7+(\sqrt7)^2`
`=16-8\sqrt7+7`
`=23-8\sqrt7`
Vậy: `(4-\sqrt7)^2=23-8\sqrt7` (đpcm)
c) `\sqrt{9-4\sqrt5}-\sqrt5=-2`
VT: `\sqrt{9-4\sqrt5}-\sqrt5`
`=\sqrt{5-2.2\sqrt5+4}-\sqrt5`
`=\sqrt{(\sqrt5-2)^2}-\sqrt5`
`=|\sqrt5-2|-\sqrt5`
`=\sqrt5-2-\sqrt5`
`=-2`
Vậy: `\sqrt{9-4\sqrt5}-\sqrt5=-2` (đpcm)
d) `\sqrt{23+8\sqrt7}-\sqrt7=4`
VT: `\sqrt{23+8\sqrt7}-\sqrt7`
`=\sqrt{16+2.4\sqrt7+7}-\sqrt7`
`=\sqrt{(4+\sqrt7)^2}-\sqrt7`
`=|4+\sqrt7|-\sqrt7`
`=4+\sqrt7-\sqrt7`
`=4`
Vậy: `\sqrt{23+8\sqrt7}-\sqrt7=4` (đpcm)