All 100 targets have a solution.
\(1 = 38 - 37 \)
\(2 = 7 - \sqrt{33 - 8 }\)
\(3 = \frac{ \sqrt{73 + 8} }{ 3 }\)
\(4 = 3! \cdot 7 - 38 \)
\(5 = \frac{ 33 + 7 }{ 8 }\)
\(6 = \sqrt{73 + 8} - 3 \)
\(7 = \sqrt{73 - 3 \cdot 8 }\)
\(8 = \sqrt{3^{8}} - 73 \)
\(9 = \sqrt{87 - 3 - 3 }\)
\(10 = 83 - 73 \)
\(11 = 3! \cdot 8 - 37 \)
\(12 = \sqrt{33 - 8} + 7 \)
\(13 = 37 - 3 \cdot 8 \)
\(14 = 38 - ( 7 - 3 )!\)
\(15 = \frac{ 37 + 8 }{ 3 }\)
\(16 = \frac{ 78 }{ 3! } + 3 \)
\(17 = 38 - 3 \cdot 7 \)
\(18 = 33 - 7 - 8 \)
\(19 = \frac{ 38 }{ \sqrt{7 - 3 } }\)
\(20 = \frac{ 78 }{ 3 } - 3 !\)
\(21 = 3 + 3 + 7 + 8 \)
\(22 = ( 3 + 7 ) \cdot 3 - 8 \)
\(23 = 7 \cdot 8 - 33 \)
\(24 = \frac{ 78 - 3! }{ 3 }\)
\(25 = \frac{ 78 - 3 }{ 3 }\)
\(26 = 37 - 3 - 8 \)
\(27 = \frac{ 73 + 8 }{ 3 }\)
\(28 = 38 - 3 - 7 \)
\(29 = \frac{ 78 }{ 3 } + 3 \)
\(30 = \frac{ 83 + 7 }{ 3 }\)
\(31 = \frac{ 87 + 3! }{ 3 }\)
\(32 = 33 + 7 - 8 \)
\(33 = ( 8 - 7 ) \cdot 33 \)
\(34 = 33 - 7 + 8 \)
\(35 = 73 - 38 \)
\(36 = 38 - \sqrt{7 - 3 }\)
\(37 = 38 + 3! - 7 \)
\(38 = ( 7 - 3! ) \cdot 38 \)
\(39 = 37 - 3! + 8 \)
\(40 = \sqrt{7 - 3} + 38 \)
\(41 = 83 - 3! \cdot 7 \)
\(42 = 37 - 3 + 8 \)
\(43 = \sqrt{\sqrt{( 3 + 3 )^{8}}} + 7 \)
\(44 = \sqrt{3^{8}} - 37 \)
\(45 = 78 - 33 \)
\(46 = 83 - 37 \)
\(47 = ( 8 - 3 )! - 73 \)
\(48 = 33 + 7 + 8 \)
\(49 = 73 - 3 \cdot 8 \)
\(50 = ( 3 + 3 ) \cdot 7 + 8 \)
\(51 = 78 - 3^{3 }\)
\(52 = ( 3 + 7 ) \cdot 3! - 8 \)
\(53 = \frac{ 3!! }{ 8 } - 37 \)
\(54 = 87 - 33 \)
\(55 = 3 \cdot 3 \cdot 7 - 8 \)
\(56 = ( 3 - 3 + 7 ) \cdot 8 \)
\(57 = \frac{ 3 }{ 3 } + 7 \cdot 8 \)
\(58 = 3! \cdot 8 + 3 + 7 \)
\(59 = 3 \cdot 7 + 38 \)
\(60 = 87 - 3^{3 }\)
\(61 = 3 \cdot 8 + 37 \)
\(62 = 73 - 3 - 8 \)
\(63 = \frac{ 378 }{ 3 ! }\)
\(64 = 8^{3 \cdot 3 - 7 }\)
\(65 = 3 \cdot 3 \cdot 8 - 7 \)
\(66 = 78 - 3! - 3 !\)
\(67 = 8^{\sqrt{7 - 3}} + 3 \)
\(68 = 73 + 3 - 8 \)
\(69 = 78 - 3 \cdot 3 \)
\(70 = 83 - 3! - 7 \)
\(71 = 73 + 3! - 8 \)
\(72 = 78 - 3 - 3 \)
\(73 = 83 - 3 - 7 \)
\(74 = ( 8 - 3! ) \cdot 37 \)
\(75 = 37 + 38 \)
\(76 = \sqrt{7 - 3} \cdot 38 \)
\(77 = 78 - \frac{ 3 }{ 3 }\)
\(78 = 73 - 3 + 8 \)
\(79 = \frac{ 3 }{ 3 } + 78 \)
\(80 = 3! \cdot 7 + 38 \)
\(81 = 87 - 3 - 3 \)
\(82 = 83 + 3! - 7 \)
\(83 = ( 8 - 3 )! - 37 \)
\(84 = 73 + 3 + 8 \)
\(85 = 3! \cdot 8 + 37 \)
\(86 = 87 - \frac{ 3 }{ 3 }\)
\(87 = ( 37 - 8 ) \cdot 3 \)
\(88 = \frac{ 3 }{ 3 } + 87 \)
\(89 = 7 \cdot 8 + 33 \)
\(90 = 87 - 3 + 3 !\)
\(91 = \frac{ 3!! - 83 }{ 7 }\)
\(92 = \frac{ 3^{3!} + 7 }{ 8 }\)
\(93 = ( 38 - 7 ) \cdot 3 \)
\(94 = \sqrt{3^{8}} + 3! + 7 \)
\(95 = ( 3! + 8 ) \cdot 7 - 3 \)
\(96 = 3 \cdot 3 + 87 \)
\(97 = 3 \cdot 8 + 73 \)
\(98 = ( 3 + 3 + 8 ) \cdot 7 \)
\(99 = 87 + 3! + 3 !\)
\(100 = ( 3 + 7 )^{8 - 3 !}\)