Đáp án:
`a)` `6\sqrt{7}`
`b)` `4\sqrt{5}-10`
`c)` `{14\sqrt{2}}/3-8\sqrt{3}`
`d)` `3\sqrt{5}+3\sqrt{7}`
Giải thích các bước giải:
`a)` `\sqrt{28}+1/3\sqrt{63}+\sqrt{175}-1/4\sqrt{448}`
`=\sqrt{2^2 . 7}+1/3 \sqrt{3^2 .7}+\sqrt{5^2 .7}-1/4\sqrt{8^2 .7}`
`=2\sqrt{7}+1/ 3 .3\sqrt{7}+5\sqrt{7}-1/4 . 8\sqrt{7}`
`=2\sqrt{7}+\sqrt{7}+5\sqrt{7}-2\sqrt{7}`
`=(2+1+5-2). \sqrt{7}`
`=6\sqrt{7}`
$\\$
`b)` `1/2\sqrt{20}+1/4\sqrt{80}-\sqrt{100}+1/3\sqrt{180}`
`=1/2\sqrt{2^2 .5}+1/4\sqrt{4^2 .5}-\sqrt{10^2}+1/3\sqrt{6^2 .5}`
`=1/ 2 .2 \sqrt{5}+1/ 4 .4\sqrt{5} -10+1/3 . 6\sqrt{5}`
`=\sqrt{5}+\sqrt{5}-10+2\sqrt{5}`
`=(1+1+2).\sqrt{5}-10`
`=4\sqrt{5}-10`
$\\$
`c)` `\sqrt{18}-\sqrt{108}+1/3\sqrt{50}-1/4\sqrt{192}`
`=\sqrt{3^2 .2}-\sqrt{6^2 .3}+1/3\sqrt{5^2 .2}-1/4\sqrt{8^2 .3}`
`=3\sqrt{2}-6\sqrt{3}+1/3 .5\sqrt{2}-1/4 .8\sqrt{3}`
`=(3\sqrt{2}+5/3\sqrt{2})-6\sqrt{3}-2\sqrt{3}`
`=(3+5/3)\sqrt{2} -(6+2)\sqrt{3}`
`={14\sqrt{2}}/3-8\sqrt{3}`
$\\$
`d)` `\sqrt{80}+1/3\sqrt{63}-1/5\sqrt{125}+\sqrt{28}`
`=\sqrt{4^2 . 5}+1/3 \sqrt{3^2 .7}-1/5\sqrt{5^2 .5}+\sqrt{2^2 .7}`
`=4\sqrt{5}+1/ 3 .3\sqrt{7}-1/5 .5\sqrt{5}+2\sqrt{7}`
`=(4\sqrt{5}-\sqrt{5})+(\sqrt{7}+2\sqrt{7})`
`=3\sqrt{5}+3\sqrt{7}`
