All 100 targets have a solution.
\(1 = ( 9 - 8 )^{15 }\)
\(2 = 9 - ( 15 - 8 )\)
\(3 = \frac{ 15 + 9 }{ 8 }\)
\(4 = 18 - 5 - 9 \)
\(5 = \sqrt{5^{\frac{ 18 }{ 9 }}}\)
\(6 = 91 - 85 \)
\(7 = \frac{ 18 }{ 9 } + 5 \)
\(8 = \sqrt{18 - 9} + 5 \)
\(9 = 8 \cdot \sqrt{9} - 15 \)
\(10 = \frac{ 18 \cdot 5 }{ 9 }\)
\(11 = \frac{ 18 }{ \sqrt{9} } + 5 \)
\(12 = \frac{ 91 + 5 }{ 8 }\)
\(13 = \frac{ 15 }{ \sqrt{9} } + 8 \)
\(14 = 95 - 81 \)
\(15 = ( 9 - 8 ) \cdot 15 \)
\(16 = 15 - 8 + 9 \)
\(17 = 1^{5} \cdot 8 + 9 \)
\(18 = \frac{ 81 + 9 }{ 5 }\)
\(19 = \frac{ 58 - 1 }{ \sqrt{9 } }\)
\(20 = 15 + 8 - \sqrt{9 }\)
\(21 = 5 \cdot 8 - 19 \)
\(22 = 81 - 59 \)
\(23 = \sqrt{81} + 5 + 9 \)
\(24 = ( 18 - 5 - 9 )!\)
\(25 = 5^{\frac{ 18 }{ 9 }}\)
\(26 = 15 + 8 + \sqrt{9 }\)
\(27 = 5 \cdot 9 - 18 \)
\(28 = \frac{ 85 - 1 }{ \sqrt{9 } }\)
\(29 = \frac{ 58 }{ \sqrt{9} - 1 }\)
\(30 = \frac{ 18 \cdot 5 }{ \sqrt{9 } }\)
\(31 = 5! - 89 \cdot 1 \)
\(32 = 15 + 8 + 9 \)
\(33 = 91 - 58 \)
\(34 = 51 - 8 - 9 \)
\(35 = ( 8 - 1^{9} ) \cdot 5 \)
\(36 = 81 - 5 \cdot 9 \)
\(37 = 15 \cdot \sqrt{9} - 8 \)
\(38 = 89 - 51 \)
\(39 = 58 - 19 \)
\(40 = \frac{ 15 \cdot 8 }{ \sqrt{9 } }\)
\(41 = 59 - 18 \)
\(42 = 18 \cdot 9 - 5 !\)
\(43 = 1 \cdot 5 \cdot 8 + \sqrt{9 }\)
\(44 = 5^{\sqrt{9}} - 81 \)
\(45 = ( 18 - 9 ) \cdot 5 \)
\(46 = 51 - 8 + \sqrt{9 }\)
\(47 = 98 - 51 \)
\(48 = ( 15 - 9 ) \cdot 8 \)
\(49 = 58 \cdot 1 - 9 \)
\(50 = 59 - \sqrt{81 }\)
\(51 = ( 9 - 8 ) \cdot 51 \)
\(52 = 51 - 8 + 9 \)
\(53 = 15 \cdot \sqrt{9} + 8 \)
\(54 = 58 - 1 - \sqrt{9 }\)
\(55 = ( 19 - 8 ) \cdot 5 \)
\(56 = 59 - \sqrt{\sqrt{81 }}\)
\(57 = 8 \cdot 9 - 15 \)
\(58 = 1^{9} \cdot 58 \)
\(59 = 5 \cdot 8 + 19 \)
\(60 = 1^{8} + 59 \)
\(61 = 58 \cdot 1 + \sqrt{9 }\)
\(62 = 59 + \sqrt{\sqrt{81 }}\)
\(63 = ( 15 - 8 ) \cdot 9 \)
\(64 = 8^{\frac{ 1 + 9 }{ 5 }}\)
\(65 = 89 - ( 5 - 1 )!\)
\(66 = 85 - 19 \)
\(67 = 58 \cdot 1 + 9 \)
\(68 = 59 + \sqrt{81 }\)
\(69 = 189 - 5 !\)
\(70 = 81 - 5 - \sqrt{9 }!\)
\(71 = 8 \cdot 9 - 1^{5 }\)
\(72 = ( 9 - 5 ) \cdot 18 \)
\(73 = 81 - 5 - \sqrt{9 }\)
\(74 = 89 - 15 \)
\(75 = 85 - 1 - 9 \)
\(76 = 85 \cdot 1 - 9 \)
\(77 = 18 + 59 \)
\(78 = 198 - 5 !\)
\(79 = 81 - 5 + \sqrt{9 }\)
\(80 = ( 1^{5} + 9 ) \cdot 8 \)
\(81 = 18 \cdot 5 - 9 \)
\(82 = 85 \cdot 1 - \sqrt{9 }\)
\(83 = 98 - 15 \)
\(84 = 85 - 1^{9 }\)
\(85 = 81 - 5 + 9 \)
\(86 = 95 - \sqrt{81 }\)
\(87 = 8 \cdot 9 + 15 \)
\(88 = 89 - 1^{5 }\)
\(89 = 1^{5} \cdot 89 \)
\(90 = 1^{5} + 89 \)
\(91 = \sqrt{5 - 1} + 89 \)
\(92 = 98 - 1 - 5 \)
\(93 = 85 - 1 + 9 \)
\(94 = 85 \cdot 1 + 9 \)
\(95 = 81 + 5 + 9 \)
\(96 = 1^{8} + 95 \)
\(97 = 98 - 1^{5 }\)
\(98 = 1^{5} \cdot 98 \)
\(99 = 18 \cdot 5 + 9 \)
\(100 = \sqrt{5 - 1} + 98 \)