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