Đáp án:
`11)` `a)` `86 `; `b)` `-13`
`12)` `a)` `A=2\sqrt{2}-2`; `b)` `B=3-\sqrt{7}`
Giải thích các bước giải:
`11)`
`a)` `\sqrt{49}.\sqrt{144}+\sqrt{256}:\sqrt{64}`
`=\sqrt{7^2}.\sqrt{12^2}+\sqrt{256: 64}`
`=7\ .\ 12+\sqrt{4}=84+2=86`
$\\$
`b)` `72: \sqrt{2^2\ . 36. 3^2}-\sqrt{225}`
`=72 : (\sqrt{2^2}.\sqrt{6^2}.\sqrt{3^2})-\sqrt{15^2}`
`=72: (2.\ 6 . \ 3 ) -15`
`=72 : 36 -15=2-15=-13`
$\\$
`12)`
`a)` `A=\sqrt{(2-\sqrt{5})^2}+\sqrt{(2\sqrt{2}-\sqrt{5})^2}`
`=|2-\sqrt{5}|+|2\sqrt{2}-\sqrt{5}|`
`=\sqrt{5}-2+2\sqrt{2}-\sqrt{5}`
(vì `2=\sqrt{4}<\sqrt{5};2\sqrt{2}=\sqrt{8}>\sqrt{5}`)
`=2\sqrt{2}-2`
Vậy `A=2\sqrt{2}-2`
$\\$
`b)` `B=\sqrt{(\sqrt{7}-2\sqrt{2})^2}+\sqrt{(3-2\sqrt{2})^2}`
`=|\sqrt{7}-2\sqrt{2}|+|3-2\sqrt{2}|`
`=2\sqrt{2}-\sqrt{7}+3-2\sqrt{2}`
(vì `2\sqrt{2}=\sqrt{8}>\sqrt{7}; 3=\sqrt{9}>2\sqrt{2}`)
`=3-\sqrt{7}`
Vậy `B=3-\sqrt{7}`
