Đáp án:
`a)\sqrt{12}-\sqrt{27}+\sqrt3`
`=\sqrt{4.3}-\sqrt{9.3}+\sqrt3`
`=2\sqrt3-3\sqrt3+\sqrt3`
`=0`
`b)\sqrt{3-\sqrt5}-\sqrt{3+\sqrt5}`
`=\sqrt{(6-2sqrt5)/2}-\sqrt{(6+2\sqrt5)/2}`
`=\sqrt{(5-2sqrt5+1)/2}-\sqrt{(5+2sqrt5+1)/2}`
`=\sqrt{(\sqrt5-1)^2/2}-\sqrt{(\sqrt5+1)^2/2}`
`=(\sqrt5-1)/\sqrt2-(sqrt5+1)/\sqrt2`
`=(sqrt5-1-sqrt5-1)/sqrt2`
`=(-2)/sqrt2`
`=-sqrt2`
`c)(\sqrt5+\sqrt3)\sqrt{8-2\sqrt{15}}`
`=(\sqrt5+sqrt3)\sqrt{5-2\sqrt{3.5}+3}`
`=(sqrt5+sqrt3)\sqrt{(\sqrt5-\sqrt3)^2}`
`=(sqrt5+sqrt3)(sqrt5-sqrt3)`
`=5-3=2`
`d)(\sqrt6+\sqrt{10})/(\sqrt{21}+\sqrt{35})`
`=(\sqrt2(\sqrt3+\sqrt5))/(\sqrt7(\sqrt3+\sqrt5))`
`=\sqrt2/\sqrt7`
`=(\sqrt{14})/7`
`e)\sqrt{(2a)/3}.\sqrt{(3a)/8}(a>=0)`
`=\sqrt{(2a.3a)/(3.8)}`
`=\sqrt{a^2/4}`
`=|a/2|`
`=a/2(do \ a>=0)`
`f)\sqrt{13a}.\sqrt{52/a}(a>0)`
`=\sqrt{(13a.52)/a}`
`=\sqrt{13.52}`
`=\sqrt{13.13.4}`
`=13.2=26`
`g)\sqrt{5a}.\sqrt{45a}-3a(a>=0)`
`=\sqrt{5a.45a}-3a`
`=\sqrt{225a^2}-3a`
`=|15a|-3a`
`=15a-3a(do \a>=0)`
`=12a`
`h)H=(3-a)^2-\sqrt{0,2}\sqrt{180a^2}`
`=9-6a+a^2-\sqrt{36a^2}`
`=9-6a+a^2-|6a|`
Nếu `a>=0`
`=>|6a|=6a`
`=>H=a^2-12a+9`
Nếu `a<=0`
`=>|6a|=-6a`
`=>H=a^2+9`.
