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Bài `1:`
`a)`
`A=sqrt(8-sqrt15).sqrt(8+sqrt15)`
`=sqrt((8-sqrt15)/1).sqrt((8+sqrt15)/1)`
`=sqrt((16-2sqrt15)/2).sqrt((16+2sqrt15)/2)`
`=sqrt((15-2sqrt15+1)/2).sqrt((15+2sqrt15+1)/2)`
`=sqrt((sqrt15-1)^2)/2.sqrt((sqrt15+1)^2)/2`
`=(|sqrt15-1|)/(sqrt2). (|sqrt15+1|)/(sqrt2)`
`=((sqrt15-1)(sqrt15+1))/(2)`
`=((sqrt15)^2-1^2)/(2)`
`=(15-1)/(2)`
`=14/(2)`
`=7`
`b)`
`B=(sqrt(6-sqrt11)+sqrt(6+sqrt11))^2`
`=(sqrt(6-sqrt11))^2+2.sqrt((6-sqrt11)(6+sqrt11))+(sqrt(6+sqrt11))^2`
`=6-sqrt11+2.sqrt(6^2-(sqrt11)^2)+6+sqrt11`
`=12+2.sqrt(36-11)`
`=12+2sqrt25`
`=12+2.5`
`=12+10`
`=22`
`c)`
`C=sqrt(2+sqrt(2+sqrt2)).sqrt(4+sqrt8).sqrt(2-sqrt(2+sqrt2))`
`=[(sqrt(2+sqrt(2+sqrt2)))(sqrt(2-sqrt(2+sqrt2)))].sqrt(4+sqrt8)`
`=sqrt((2+sqrt(2+sqrt2))(2-sqrt(2+sqrt2))).sqrt(4+sqrt8)`
`=sqrt(2^2-(sqrt(2+sqrt2))^2).sqrt(4+sqrt8)`
`=sqrt(4-2-sqrt2).sqrt(4+sqrt8)`
`=sqrt(2-sqrt2).sqrt(4+2sqrt2)`
`=sqrt((2-sqrt2)(4+2sqrt2))`
`=sqrt((2-sqrt2).2.(2+sqrt2))`
`=sqrt2.sqrt((2-sqrt2)(2+sqrt2))`
`=sqrt2.sqrt(4-2)`
`=sqrt2.sqrt2`
`=sqrt4`
`=2`
`d)`
`D=sqrt(10+2sqrt21)-sqrt3`
`=sqrt(7+2sqrt7. sqrt3+3)-sqrt3`
`=sqrt((sqrt7+sqrt3)^2)-sqrt3`
`=|sqrt7+sqrt3|-sqrt3`
`=sqrt7+sqrt3-sqrt3`
`=sqrt7`
`#owen`
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1294
$a,\sqrt{8-\sqrt{15}}.\sqrt{8+\sqrt{15}}\\
=\sqrt{\left(8-\sqrt{15}\right)\left(8+\sqrt{15}\right)}\\
=\sqrt{64-15}\\
=\sqrt{49}\\
=7\\
b,\left(\sqrt{6-\sqrt{11}}+\sqrt{6+\sqrt{11}}\right)^2\\
=6-\sqrt{11}+6+\sqrt{11}+2\sqrt{\left(6-\sqrt{11}\right)\left(6+\sqrt{11}\right)}\\
=12+2\sqrt{36-11}\\
=12+2\sqrt{25}\\
=12+2.5\\
=22\\
c,\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{4+\sqrt{8}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\\
=\sqrt{2+\sqrt{2+\sqrt{2}}}\sqrt{2-\sqrt{2+\sqrt{2}}}.\sqrt{4+2\sqrt{2}}\\
=\sqrt{4-\left(2+\sqrt{2}\right)}.\sqrt{2\left(2+\sqrt{2}\right)}\\
=\sqrt{2}.\sqrt{2-\sqrt{2}}\sqrt{2+\sqrt{2}}\\
=\sqrt{2}\sqrt{4-2}\\
=\sqrt{2}.\sqrt{2}\\
=2\\
d,\sqrt{10+2\sqrt{21}}-\sqrt{3}\\
=\sqrt{7+2\sqrt{7}.\sqrt{3}+3}-\sqrt{3}\\ =\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}-\sqrt{3}\\
=\sqrt{7}+\sqrt{3}-\sqrt{3}\\
=\sqrt{7}$
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