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