All 100 targets have a solution.
\(1 = 69^{8 - 8 }\)
\(2 = \sqrt{\frac{ 68 }{ 8 + 9 }}\)
\(3 = 89 - 86 \)
\(4 = \frac{ 68 }{ 8 + 9 }\)
\(5 = 69 - 8 \cdot 8 \)
\(6 = ( 89 - 86 )!\)
\(7 = \frac{ 98 }{ 6 + 8 }\)
\(8 = 96 - 88 \)
\(9 = ( 8 - 8 ) \cdot 6 + 9 \)
\(10 = \sqrt{98 - 6 + 8 }\)
\(11 = \sqrt{\frac{ 968 }{ 8 }}\)
\(12 = 98 - 86 \)
\(13 = \sqrt{889 - 6 !}\)
\(14 = 86 - 8 \cdot 9 \)
\(15 = \frac{ 98 - 8 }{ 6 }\)
\(16 = \frac{ 8 }{ 8 } + 6 + 9 \)
\(17 = \sqrt{8^{8 - 6}} + 9 \)
\(18 = \sqrt{\sqrt{89 - 8}} \cdot 6 \)
\(19 = 88 - 69 \)
\(20 = \frac{ 96 }{ 8 } + 8 \)
\(21 = 89 - 68 \)
\(22 = \sqrt{98 \cdot 8} - 6 \)
\(23 = \sqrt{8 \cdot 8} + 6 + 9 \)
\(24 = ( \frac{ 68 }{ 8 + 9 } )!\)
\(25 = ( 8 - 6 ) \cdot 8 + 9 \)
\(26 = \frac{ 86 - 8 }{ \sqrt{9 } }\)
\(27 = \sqrt{\sqrt{\sqrt{89 - 8}}^{6 }}\)
\(28 = \frac{ 6^{\sqrt{9}} + 8 }{ 8 }\)
\(29 = \frac{ \frac{ 6! }{ \sqrt{9} } - 8 }{ 8 }\)
\(30 = 98 - 68 \)
\(31 = 6 + 8 + 8 + 9 \)
\(32 = 96 - 8 \cdot 8 \)
\(33 = 89 - \frac{ 8! }{ 6 ! }\)
\(34 = 88 - 6 \cdot 9 \)
\(35 = \frac{ 6^{\sqrt{9}} }{ 8 } + 8 \)
\(36 = \frac{ 8 }{ 8 - 6 } \cdot 9 \)
\(37 = 6 \cdot 8 - 8 - \sqrt{9 }\)
\(38 = 6 \cdot 9 - 8 - 8 \)
\(39 = \sqrt{8 \cdot 8} \cdot 6 - 9 \)
\(40 = ( 6 + 8 - 9 ) \cdot 8 \)
\(41 = 89 - 6 \cdot 8 \)
\(42 = ( 8 + 8 - 9 ) \cdot 6 \)
\(43 = \frac{ 86 }{ 8 - \sqrt{9 }! }\)
\(44 = 68 - 8 \cdot \sqrt{9 }\)
\(45 = \frac{ 8! }{ 896 }\)
\(46 = ( 8 - \sqrt{9} ) \cdot 8 + 6 \)
\(47 = 6 \cdot 8 + 8 - 9 \)
\(48 = ( 9 - 8 ) \cdot 6 \cdot 8 \)
\(49 = \frac{ 98 }{ 8 - 6 }\)
\(50 = 98 - 6 \cdot 8 \)
\(51 = 68 - 8 - 9 \)
\(52 = ( 8 - \sqrt{9} )! - 68 \)
\(53 = 69 - 8 - 8 \)
\(54 = \sqrt{89 - 8} \cdot 6 \)
\(55 = 8^{8 - 6} - 9 \)
\(56 = ( 9 - ( 8 - 6 ) ) \cdot 8 \)
\(57 = 68 - 8 - \sqrt{9 }\)
\(58 = 8 \cdot 9 - 6 - 8 \)
\(59 = 68 - \frac{ 9! }{ 8 ! }\)
\(60 = ( \frac{ 8 }{ 8 } + 9 ) \cdot 6 \)
\(61 = 69 - \sqrt{8 \cdot 8 }\)
\(62 = 86 - 8 \cdot \sqrt{9 }\)
\(63 = 68 - 8 + \sqrt{9 }\)
\(64 = 98 \cdot 8 - 6 !\)
\(65 = 69 - \sqrt{8 + 8 }\)
\(66 = 68 - 8 + \sqrt{9 }!\)
\(67 = 68 + 8 - 9 \)
\(68 = ( 9 - 8 ) \cdot 68 \)
\(69 = 68 - 8 + 9 \)
\(70 = \frac{ 8 }{ 8 } + 69 \)
\(71 = \sqrt{\sqrt{8 + 8}} + 69 \)
\(72 = 88 \cdot 9 - 6 !\)
\(73 = 88 - 6 - 9 \)
\(74 = 8 \cdot 9 - 6 + 8 \)
\(75 = 89 - 6 - 8 \)
\(76 = 88 - 6 - \sqrt{9 }!\)
\(77 = \sqrt{8 \cdot 8} + 69 \)
\(78 = ( \sqrt{8 + 8} + 9 ) \cdot 6 \)
\(79 = 68 + 8 + \sqrt{9 }\)
\(80 = 96 - 8 - 8 \)
\(81 = 86 - 8 + \sqrt{9 }\)
\(82 = 88 - ( 9 - 6 )!\)
\(83 = \sqrt{6889 }\)
\(84 = 98 - 6 - 8 \)
\(85 = 68 + 8 + 9 \)
\(86 = ( 9 - 8 ) \cdot 86 \)
\(87 = 86 - 8 + 9 \)
\(88 = \sqrt{968 \cdot 8 }\)
\(89 = \sqrt{89^{8 - 6 }}\)
\(90 = \frac{ 6 }{ \sqrt{9} } + 88 \)
\(91 = 88 - 6 + 9 \)
\(92 = 8 \cdot \sqrt{9} + 68 \)
\(93 = \sqrt{8 + 8}! + 69 \)
\(94 = ( 9 - 6 )! + 88 \)
\(95 = 96 - \frac{ 8 }{ 8 }\)
\(96 = \frac{ 96 }{ 8 } \cdot 8 \)
\(97 = \frac{ 8 }{ 8 } + 96 \)
\(98 = \sqrt{98^{8 - 6 }}\)
\(99 = ( 8 + 8 ) \cdot 6 + \sqrt{9 }\)
\(100 = 98 - 6 + 8 \)