Đáp án:
`a)` `{199\sqrt{6}}/6`
`b)` `-2\sqrt{2}`
`d)` `3.(1-\sqrt{2})`
`e)` ` -4`
Giải thích các bước giải:
`a)` `\sqrt{54}-\sqrt{3/2}+5\sqrt{216}+\sqrt{8/3}`
`=\sqrt{3^2 . 6}-\sqrt{6/{2^2}}+5\sqrt{6^2 .6}+\sqrt{{8.3}/{3^2}}`
`=3\sqrt{6}-1/ 2 \sqrt{6}+5.6\sqrt{6}+2/ 3 \sqrt{6}`
`=(3-1/2 +30+2/3).\sqrt{6}`
`={199\sqrt{6}}/6`
$\\$
`b)` `\sqrt{8-2\sqrt{12}}-\sqrt{8+2\sqrt{12}}`
`=\sqrt{6-2.\sqrt{6}.\sqrt{2}+2}-\sqrt{6+2.\sqrt{6}.\sqrt{2}+2}`
`=\sqrt{(\sqrt{6}-\sqrt{2})^2}-\sqrt{(\sqrt{6}+\sqrt{2})^2}`
`=\sqrt{6}-\sqrt{2}-(\sqrt{6}+\sqrt{2})`
`=-2\sqrt{2}`
$\\$
`d)` `\root[3]{189-135\sqrt{2}}`
`=\root[3]{3^3 (7-5\sqrt{2})}`
`=3\root[3]{7-5\sqrt{2}}`
`=3\root[3]{1-3\sqrt{2}+6-2\sqrt{2}}`
`=3\root[3]{1^3-3.1^2 .\sqrt{2}+3.1.(\sqrt{2})^2-(\sqrt{2})^3}`
`=3\root[3]{(1-\sqrt{2})^3}`
`=3.(1-\sqrt{2})`
$\\$
`e)` `{5\sqrt{3}-3\sqrt{5}}/{\sqrt{5}-\sqrt{3}}-2/{\sqrt{5}-2}+\sqrt{5}/{\sqrt{3}+2}`
`={\sqrt{3}.\sqrt{5}.(\sqrt{5}-\sqrt{3})}/{\sqrt{5}-\sqrt{3}}-{2(\sqrt{5}+2)}/{(\sqrt{5}-2)(\sqrt{5}+2)}+{\sqrt{5}(2-\sqrt{3})}/{(2+\sqrt{3})(2-\sqrt{3})}`
`=\sqrt{15} - {2(\sqrt{5}+2)}/{5-2^2} +{\sqrt{5}.(2-\sqrt{3})}/{2^2-3}`
`=\sqrt{15}-2\sqrt{5}-4+2\sqrt{5}-\sqrt{15}`
`=-4`
