All 100 targets have a solution.
\(1 = 14^{8 - 8 }\)
\(2 = 8 - ( 14 - 8 )\)
\(3 = 84 - 81 \)
\(4 = \sqrt{18 - \frac{ 8 }{ 4 }}\)
\(5 = \frac{ 48 }{ 8 } - 1 \)
\(6 = ( 84 - 81 )!\)
\(7 = \frac{ 48 }{ 8 } + 1 \)
\(8 = 18 - \sqrt{4} - 8 \)
\(9 = \frac{ 18 \cdot 4 }{ 8 }\)
\(10 = 14 - \sqrt{8 + 8 }\)
\(11 = \frac{ 8 }{ 4 } + \sqrt{81 }\)
\(12 = \frac{ 84 }{ 8 - 1 }\)
\(13 = 14 - \frac{ 8 }{ 8 }\)
\(14 = 14 - 8 + 8 \)
\(15 = \frac{ 8 }{ 8 } + 14 \)
\(16 = 18 - \frac{ 8 }{ 4 }\)
\(17 = \frac{ 18 }{ \sqrt{4} } + 8 \)
\(18 = \sqrt{8 + 8} + 14 \)
\(19 = 4 - 1 + 8 + 8 \)
\(20 = \frac{ 8 }{ 4 } + 18 \)
\(21 = \sqrt{841} - 8 \)
\(22 = 18 - 4 + 8 \)
\(23 = \frac{ 184 }{ 8 }\)
\(24 = 18 - \sqrt{4} + 8 \)
\(25 = 41 - 8 - 8 \)
\(26 = \sqrt{81 \cdot 4} + 8 \)
\(27 = \frac{ 81 \cdot 8 }{ 4 ! }\)
\(28 = \frac{ 84 }{ \sqrt{\sqrt{81 }} }\)
\(29 = \sqrt{\frac{ 8! }{ 48 } + 1 }\)
\(30 = 48 - 18 \)
\(31 = ( 8 - 4 ) \cdot 8 - 1 \)
\(32 = ( 1 + 4 )! - 88 \)
\(33 = 81 - 48 \)
\(34 = 18 + 4! - 8 \)
\(35 = 4 \cdot 8 + \sqrt{\sqrt{81 }}\)
\(36 = \frac{ 18 \cdot 8 }{ 4 }\)
\(37 = \sqrt{841} + 8 \)
\(38 = \sqrt{8 + 8}! + 14 \)
\(39 = 48 - \sqrt{81 }\)
\(40 = ( 18 - 8 ) \cdot 4 \)
\(41 = 41 - 8 + 8 \)
\(42 = \frac{ 8 }{ 8 } + 41 \)
\(43 = \frac{ 88 }{ \sqrt{4} } - 1 \)
\(44 = 18 \cdot \sqrt{4} + 8 \)
\(45 = 48 - \sqrt{\sqrt{81 }}\)
\(46 = 8^{\sqrt{4}} - 18 \)
\(47 = \frac{ 188 }{ 4 }\)
\(48 = ( 14 - 8 ) \cdot 8 \)
\(49 = 1^{8} + 48 \)
\(50 = 8 \cdot 8 - 14 \)
\(51 = 48 + \sqrt{\sqrt{81 }}\)
\(52 = ( 18 + 8 ) \cdot \sqrt{4 }\)
\(53 = \sqrt{\sqrt{( 8 - 1 )^{8}}} + 4 \)
\(54 = \frac{ 18 \cdot 4! }{ 8 }\)
\(55 = 48 - 1 + 8 \)
\(56 = 48 \cdot 1 + 8 \)
\(57 = 48 + \sqrt{81 }\)
\(58 = ( 8 - 1 ) \cdot 8 + \sqrt{4 }\)
\(59 = 8 \cdot 8 - 1 - 4 \)
\(60 = \frac{ ( 8 - 1 )! }{ 84 }\)
\(61 = 8 \cdot 8 + 1 - 4 \)
\(62 = 1 \cdot 8 \cdot 8 - \sqrt{4 }\)
\(63 = 88 - 1 - 4 !\)
\(64 = 18 \cdot 4 - 8 \)
\(65 = 81 - 4! + 8 \)
\(66 = 18 + 48 \)
\(67 = 8 \cdot 8 - 1 + 4 \)
\(68 = ( \sqrt{81} + 8 ) \cdot 4 \)
\(69 = 81 - 4 - 8 \)
\(70 = \sqrt{81} \cdot 8 - \sqrt{4 }\)
\(71 = 81 - \sqrt{4} - 8 \)
\(72 = ( 8 - 4 ) \cdot 18 \)
\(73 = \sqrt{\sqrt{81}}^{4} - 8 \)
\(74 = 88 - 14 \)
\(75 = 84 - \sqrt{81 }\)
\(76 = 84 \cdot 1 - 8 \)
\(77 = 81 + 4 - 8 \)
\(78 = 8 \cdot 8 + 14 \)
\(79 = 81 - \frac{ 8 }{ 4 }\)
\(80 = 18 \cdot 4 + 8 \)
\(81 = 84 - \sqrt{\sqrt{81 }}\)
\(82 = 8^{\sqrt{4}} + 18 \)
\(83 = \frac{ 8 }{ 4 } + 81 \)
\(84 = 1^{8} \cdot 84 \)
\(85 = 81 - 4 + 8 \)
\(86 = 88 \cdot 1 - \sqrt{4 }\)
\(87 = 88 - 1^{4 }\)
\(88 = 1^{4} \cdot 88 \)
\(89 = 1^{4} + 88 \)
\(90 = \frac{ ( 14 - 8 )! }{ 8 }\)
\(91 = 84 - 1 + 8 \)
\(92 = 84 \cdot 1 + 8 \)
\(93 = \sqrt{81} + 84 \)
\(94 = \frac{ 188 }{ \sqrt{4 } }\)
\(95 = ( 4 + 8 ) \cdot 8 - 1 \)
\(96 = ( 1 \cdot 4 + 8 ) \cdot 8 \)
\(97 = 81 + 4! - 8 \)
\(98 = \frac{ ( 4 - 1 )!! }{ 8 } + 8 \)
\(99 = \sqrt{\sqrt{( \sqrt{4} + 8 )^{8}}} - 1 \)
\(100 = ( 18 - 8 )^{\sqrt{4 }}\)