Đáp án:
`a)` `5\sqrt{2}-6\sqrt{7}`
`b)` `3`
`c)` `-\sqrt{2}`
Giải thích các bước giải:
`a)` `\sqrt{25.2}-\sqrt{700}+\sqrt{1008} -\sqrt{448}`
`=\sqrt{5^2. 2}-\sqrt{10^2 . 7}+\sqrt{12^2 .7}-\sqrt{8^2 .7}`
`=5\sqrt{2}-10\sqrt{7}+12\sqrt{7}-8\sqrt{7}`
`=5\sqrt{2}-(10-12+8)\sqrt{7}`
`=5\sqrt{2}-6\sqrt{7}`
Vậy `\sqrt{25.2}-\sqrt{700}+\sqrt{1008} -\sqrt{448}`
`=5\sqrt{2}-6\sqrt{7}`
$\\$
`b)` `\sqrt{3}.(\sqrt{12}-\sqrt{8}-\sqrt{3})+\sqrt{24}`
`=\sqrt{3.12}-\sqrt{3.8}-\sqrt{3.3}+\sqrt{24}`
`=\sqrt{6^2}-\sqrt{24}-\sqrt{3^2}+\sqrt{24}`
`=6-3+\sqrt{24}-\sqrt{24}=3`
Vậy: `\sqrt{3}.(\sqrt{12}-\sqrt{8}-\sqrt{3})+\sqrt{24}=3`
$\\$
`c)` `\sqrt{8-\sqrt{15}}-\sqrt{8+\sqrt{15}}`
`=\sqrt{{16-2\sqrt{15}}/2}-\sqrt{{16+2\sqrt{15}}/2}`
`=\sqrt{{15-2\sqrt{15}.1+1^2}/2}-\sqrt{{15+2\sqrt{15}.1+1^2}/2}`
`=\sqrt{{(\sqrt{15}-1)^2}/2}-\sqrt{{(\sqrt{15}+1)^2}/2}`
`=|\sqrt{15}-1|/\sqrt{2}-|\sqrt{15}+1|/\sqrt{2}`
`={\sqrt{15}-1-(\sqrt{15}+1)}/\sqrt{2}`
`={-2}/\sqrt{2}=-\sqrt{2}`
Vậy: `\sqrt{8-\sqrt{15}}-\sqrt{8+\sqrt{15}}=-\sqrt{2}`