4 6 8 9

All 100 targets have a solution.

\(1 = 9 - \frac{ 48 }{ 6 }\)
\(2 = \frac{ 96 }{ 48 }\)
\(3 = \frac{ \frac{ 96 }{ 4 } }{ 8 }\)
\(4 = \sqrt{\frac{ 48 }{ 9 - 6 }}\)
\(5 = \sqrt{89 - 64 }\)
\(6 = \frac{ 46 + 8 }{ 9 }\)
\(7 = 8 - ( \sqrt{49} - 6 )\)
\(8 = 94 - 86 \)
\(9 = \sqrt{89 - \sqrt{64 }}\)
\(10 = \frac{ 84 + 6 }{ 9 }\)
\(11 = \frac{ 94 - 6 }{ 8 }\)
\(12 = 96 - 84 \)
\(13 = 9^{\sqrt{4}} - 68 \)
\(14 = \frac{ 48 - 6 }{ \sqrt{9 } }\)
\(15 = 84 - 69 \)
\(16 = \frac{ 48 }{ 9 - 6 }\)
\(17 = \frac{ 48 }{ 6 } + 9 \)
\(18 = \frac{ 46 + 8 }{ \sqrt{9 } }\)
\(19 = 68 - 49 \)
\(20 = \frac{ 68 }{ 4 } + \sqrt{9 }\)
\(21 = 69 - 48 \)
\(22 = \frac{ 96 - 8 }{ 4 }\)
\(23 = \frac{ 84 }{ 6 } + 9 \)
\(24 = \frac{ 96 }{ 8 - 4 }\)
\(25 = 89 - 64 \)
\(26 = 94 - 68 \)
\(27 = \frac{ 4 \cdot 6 }{ 8 } \cdot 9 \)
\(28 = \frac{ 84 }{ 9 - 6 }\)
\(29 = 46 - 8 - 9 \)
\(30 = \sqrt{894 + 6 }\)
\(31 = \frac{ 68 }{ \sqrt{4} } - \sqrt{9 }\)
\(32 = \frac{ 48 \cdot 6 }{ 9 }\)
\(33 = 48 - 6 - 9 \)
\(34 = 98 - 64 \)
\(35 = 49 - 6 - 8 \)
\(36 = \sqrt{9}!! - 684 \)
\(37 = 86 - 49 \)
\(38 = ( 9 - 4 ) \cdot 6 + 8 \)
\(39 = 48 - 6 - \sqrt{9 }\)
\(40 = 64 - 8 \cdot \sqrt{9 }\)
\(41 = 46 - 8 + \sqrt{9 }\)
\(42 = 48 - ( 9 - 6 )!\)
\(43 = 89 - 46 \)
\(44 = \sqrt{968 \cdot \sqrt{4 }}\)
\(45 = 46 + 8 - 9 \)
\(46 = ( 9 - 8 ) \cdot 46 \)
\(47 = 46 - 8 + 9 \)
\(48 = 96 - 48 \)
\(49 = \frac{ 98 }{ 6 - 4 }\)
\(50 = 86 - 4 \cdot 9 \)
\(51 = 48 - 6 + 9 \)
\(52 = \frac{ 468 }{ 9 }\)
\(53 = 64 - 8 - \sqrt{9 }\)
\(54 = \frac{ 486 }{ 9 }\)
\(55 = 68 - 4 - 9 \)
\(56 = \frac{ 84 \cdot 6 }{ 9 }\)
\(57 = 69 - 4 - 8 \)
\(58 = 6 \cdot 9 - 4 + 8 \)
\(59 = 64 - 8 + \sqrt{9 }\)
\(60 = ( 8 - 4 ) \cdot ( 6 + 9 )\)
\(61 = 68 - \sqrt{49 }\)
\(62 = \frac{ 496 }{ 8 }\)
\(63 = 46 + 8 + 9 \)
\(64 = ( 9 - 8 ) \cdot 64 \)
\(65 = 64 - 8 + 9 \)
\(66 = 6 \cdot \sqrt{9} + 48 \)
\(67 = 69 - \frac{ 8 }{ 4 }\)
\(68 = ( 4 - \sqrt{9} ) \cdot 68 \)
\(69 = 84 - 6 - 9 \)
\(70 = 8 \cdot \sqrt{9} + 46 \)
\(71 = \frac{ 8 }{ 4 } + 69 \)
\(72 = \frac{ 648 }{ 9 }\)
\(73 = 68 - 4 + 9 \)
\(74 = 98 - 4 \cdot 6 \)
\(75 = \sqrt{49} + 68 \)
\(76 = \frac{ 684 }{ 9 }\)
\(77 = 89 - \sqrt{4} \cdot 6 \)
\(78 = \frac{ 468 }{ \sqrt{9 }! }\)
\(79 = 86 - \sqrt{49 }\)
\(80 = 94 - 6 - 8 \)
\(81 = 89 - \sqrt{64 }\)
\(82 = 84 - \frac{ 6 }{ \sqrt{9 } }\)
\(83 = \frac{ 498 }{ 6 }\)
\(84 = 96 - 4 - 8 \)
\(85 = 69 + 4! - 8 \)
\(86 = \sqrt{4} \cdot 9 + 68 \)
\(87 = 84 - 6 + 9 \)
\(88 = 98 - 4 - 6 \)
\(89 = \sqrt{89^{6 - 4 }}\)
\(90 = 98 - \sqrt{64 }\)
\(91 = 86 - 4 + 9 \)
\(92 = 94 + 6 - 8 \)
\(93 = \sqrt{8649 }\)
\(94 = \frac{ 846 }{ 9 }\)
\(95 = 98 - \frac{ 6 }{ \sqrt{4 } }\)
\(96 = \frac{ 864 }{ 9 }\)
\(97 = \sqrt{64} + 89 \)
\(98 = ( 8 - 6 ) \cdot 49 \)
\(99 = 84 + 6 + 9 \)
\(100 = 96 - 4 + 8 \)