Đáp án:
`a)` `-4\sqrt{2}`
`b)` `6\sqrt{3}+3\sqrt{5}`
`c)` `-42\sqrt{6}`
Giải thích các bước giải:
`a)` `\sqrt{8}-3\sqrt{32}+\sqrt{72}`
`=\sqrt{2^2 .2}-3\sqrt{4^2 .2}+\sqrt{6^2 .2}`
`=2\sqrt{2}-3.4\sqrt{2}+6\sqrt{2}`
`=(2-12+6).\sqrt{2}=-4\sqrt{2}`
Vậy: ` \sqrt{8}-3\sqrt{32}+\sqrt{72}=-4\sqrt{2}`
$\\$
`b)` `6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}`
`=6\sqrt{2^2 .3}-\sqrt{2^2 .5}-2\sqrt{3^2 .3}+\sqrt{5^2 .5}`
`=6.2\sqrt{3}-2\sqrt{5}-2.3\sqrt{3}+5\sqrt{5}`
`=(12\sqrt{3}-6\sqrt{3})+(-2\sqrt{5}+5\sqrt{5})`
`=6\sqrt{3}+3\sqrt{5}`
Vậy: `6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}=6\sqrt{3}+3\sqrt{5}`
$\\$
`c)` `3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}`
`=3\sqrt{4^2 .7}-7\sqrt{6^2 .6}+4\sqrt{3^2 .6}-2\sqrt{6^2 .7}-3\sqrt{4^2 .6}`
`=3.4\sqrt{7}-7.6\sqrt{6}+4.3\sqrt{6}-2.6\sqrt{7}-3.4\sqrt{6}`
`=(12\sqrt{7}-12\sqrt{7})+(-42\sqrt{6}+12\sqrt{6}-12\sqrt{6})`
`=-42\sqrt{6}`
Vậy: `3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}=-42\sqrt{6}`
