Lời giải :
`a)\sqrt{(\sqrt{7}-3)^2}+\sqrt{4+2\sqrt{7}}`
`=|\sqrt{7}-3|+|4+2\sqrt{7}|`
`=3-\sqrt{7}+4+2\sqrt{7}`
`=5+\sqrt{7}`
`b)\sqrt{(2\sqrt{10}-7)^2}-\sqrt{59+14\sqrt{10)`
`=7-2\sqrt{10}-\sqrt{7^2+10+2.7.\sqrt{10}}`
`=7-2\sqrt{10}-\sqrt{(7+\sqrt{10})^2}`
`=7-2\sqrt{10}-7-\sqrt{10}`
`=-3\sqrt{10}`
`c)\sqrt{6-2\sqrt{5}}+\sqrt{21+4\sqrt{5}}`
`=\sqrt{5+1-2.1.\sqrt{5}}+\sqrt{(2\sqrt{5})^2+1+2.2\sqrt{5}}`
`=\sqrt{(\sqrt{5}-1)^2}+\sqrt{(2\sqrt{5}+1)^2}`
`=\sqrt{5}-1+2\sqrt{5}+1`
`=3\sqrt{5}`
`d)\sqrt{43+24\sqrt{3}}-\sqrt{52-30\sqrt{3}}`
`=\sqrt{(3\sqrt{3})^2+4^2+2.4.3\sqrt{3}}-\sqrt{(3\sqrt{3})^2+5^2-2.5.3\sqrt{3}}`
`=\sqrt{(3\sqrt{3}+4)^2}-\sqrt{(3\sqrt{3}-5)^2}`
`=3\sqrt{3}+4-|3\sqrt{3}-5|`
`=3\sqrt{3}+4-3\sqrt{3}+5`
`=9`
