Bài `15` :
`a) 9+4\sqrt{5}`
`=5+4\sqrt{5}+4`
`=(\sqrt{5})^2+2*\sqrt{5}*2+2^2`
`=(\sqrt{5}+2)^2`
`b) \sqrt{9-4\sqrt{5}}-\sqrt{5}`
`=\sqrt{5-4\sqrt{5}+4}-\sqrt{5}`
`=\sqrt{(\sqrt{5})^2-2*\sqrt{5}*2+2^2}-\sqrt{5}`
`=\sqrt{(\sqrt{5}-2)^2}-\sqrt{5}`
`=|\sqrt{5}-2| -\sqrt{5}`
`=\sqrt{5}-\sqrt{5}-2`
`=-2`
`c) (4-\sqrt{7})^2`
`=4^2-2*4*\sqrt{7}+(\sqrt{7})^2`
`=16-8\sqrt{7}+7`
`=23-8\sqrt{7}`
`d) \sqrt{23+8\sqrt{7}-\sqrt{7}`
`=\sqrt{16+8\sqrt{7}+7}-\sqrt{7}`
`=\sqrt{4^2+2*4*\sqrt{7}+(\sqrt{7})^2}-\sqrt{7}`
`=\sqrt{(4+\sqrt{7})^2}-\sqrt{7}`
`=4+\sqrt{7}-\sqrt{7}`
`=4`
