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