All 100 targets have a solution.
\(1 = 1^{\sqrt{484 }}\)
\(2 = 14 - 4 - 8 \)
\(3 = \frac{ 14 - 8 }{ \sqrt{4 } }\)
\(4 = \sqrt{144} - 8 \)
\(5 = \sqrt{\sqrt{841} - 4 }\)
\(6 = \frac{ 84 }{ 14 }\)
\(7 = 48 - 41 \)
\(8 = 14 + \sqrt{4} - 8 \)
\(9 = 41 - 4 \cdot 8 \)
\(10 = 14 + 4 - 8 \)
\(11 = \frac{ 48 }{ 4 } - 1 \)
\(12 = \sqrt{148 - 4 }\)
\(13 = \sqrt{441} - 8 \)
\(14 = \sqrt{14^{\frac{ 8 }{ 4 }}}\)
\(15 = \frac{ 14 }{ \sqrt{4} } + 8 \)
\(16 = \frac{ 8 }{ 4 } + 14 \)
\(17 = 18 - \frac{ 4 }{ 4 }\)
\(18 = \frac{ 144 }{ 8 }\)
\(19 = \frac{ 4 }{ 4 } + 18 \)
\(20 = \sqrt{144} + 8 \)
\(21 = \sqrt{484} - 1 \)
\(22 = \sqrt{484} \cdot 1 \)
\(23 = \sqrt{484} + 1 \)
\(24 = ( 14 - 8 ) \cdot 4 \)
\(25 = \sqrt{841} - 4 \)
\(26 = 44 - 18 \)
\(27 = \sqrt{841} - \sqrt{4 }\)
\(28 = \frac{ 14 \cdot 8 }{ 4 }\)
\(29 = \sqrt{441} + 8 \)
\(30 = 14 + 4! - 8 \)
\(31 = \sqrt{841} + \sqrt{4 }\)
\(32 = 18 \cdot \sqrt{4} - 4 \)
\(33 = \sqrt{841} + 4 \)
\(34 = 48 - 14 \)
\(35 = 44 - \sqrt{81 }\)
\(36 = 44 \cdot 1 - 8 \)
\(37 = \frac{ 148 }{ 4 }\)
\(38 = ( 8 - 4 )! + 14 \)
\(39 = 41 - \frac{ 8 }{ 4 }\)
\(40 = 18 \cdot \sqrt{4} + 4 \)
\(41 = 44 - \sqrt{\sqrt{81 }}\)
\(42 = \frac{ 14 \cdot 4! }{ 8 }\)
\(43 = 84 - 41 \)
\(44 = 1^{8} \cdot 44 \)
\(45 = 41 - 4 + 8 \)
\(46 = \frac{ 184 }{ 4 }\)
\(47 = 48 - 1^{4 }\)
\(48 = 14 \cdot 4 - 8 \)
\(49 = 1^{4} + 48 \)
\(50 = 8^{\sqrt{4}} - 14 \)
\(51 = 44 - 1 + 8 \)
\(52 = 44 \cdot 1 + 8 \)
\(53 = 44 + \sqrt{81 }\)
\(54 = ( 4 - 1 )! + 48 \)
\(55 = 81 - 4! - \sqrt{4 }\)
\(56 = ( 8 - 4 ) \cdot 14 \)
\(57 = 41 + 4! - 8 \)
\(58 = \sqrt{841 \cdot 4 }\)
\(59 = 84 - 1 - 4 !\)
\(60 = 84 \cdot 1 - 4 !\)
\(61 = 81 - 4! + 4 \)
\(62 = 14 + 48 \)
\(63 = ( 4 + 4 ) \cdot 8 - 1 \)
\(64 = 14 \cdot 4 + 8 \)
\(65 = 81 - 4 \cdot 4 \)
\(66 = ( 41 - 8 ) \cdot \sqrt{4 }\)
\(67 = 8^{\sqrt{4}} - 1 + 4 \)
\(68 = 18 \cdot 4 - 4 \)
\(69 = 81 - \frac{ 4! }{ \sqrt{4 } }\)
\(70 = 84 - 14 \)
\(71 = 48 - 1 + 4 !\)
\(72 = \sqrt{4 \cdot 4} \cdot 18 \)
\(73 = 4 \cdot 8 + 41 \)
\(74 = \frac{ 148 }{ \sqrt{4 } }\)
\(75 = 81 - 4 - \sqrt{4 }\)
\(76 = 18 \cdot 4 + 4 \)
\(77 = 81 - \sqrt{4 \cdot 4 }\)
\(78 = 8^{\sqrt{4}} + 14 \)
\(79 = 84 - 1 - 4 \)
\(80 = ( 14 - 4 ) \cdot 8 \)
\(81 = 81 - 4 + 4 \)
\(82 = \frac{ 41 \cdot 8 }{ 4 }\)
\(83 = 84 - 1^{4 }\)
\(84 = 1^{4} \cdot 84 \)
\(85 = 1^{4} + 84 \)
\(86 = 84 \cdot 1 + \sqrt{4 }\)
\(87 = 84 - 1 + 4 \)
\(88 = ( 14 + 8 ) \cdot 4 \)
\(89 = 41 + 48 \)
\(90 = 41 \cdot \sqrt{4} + 8 \)
\(91 = \frac{ ( \sqrt{4} + 4 )! }{ 8 } + 1 \)
\(92 = \frac{ 184 }{ \sqrt{4 } }\)
\(93 = \frac{ 4! }{ \sqrt{4} } + 81 \)
\(94 = ( 48 - 1 ) \cdot \sqrt{4 }\)
\(95 = 48 \cdot \sqrt{4} - 1 \)
\(96 = \sqrt{144} \cdot 8 \)
\(97 = 4 \cdot 4 + 81 \)
\(98 = 14 + 84 \)
\(99 = 4 \cdot 4! + \sqrt{\sqrt{81 }}\)
\(100 = \sqrt{\sqrt{( 14 - 4 )^{8 }}}\)