All 100 targets have a solution.
\(1 = 96 - 95 \)
\(2 = \frac{ 5! }{ 69 - 9 }\)
\(3 = \sqrt{\frac{ 99 }{ 5 + 6 }}\)
\(4 = \sqrt{9 \cdot 9 - 65 }\)
\(5 = 59 - 6 \cdot 9 \)
\(6 = 9 - \frac{ 6 + 9 }{ 5 }\)
\(7 = 9 - ( 5 + 6 - 9 )\)
\(8 = \sqrt{65 - \frac{ 9 }{ 9 }}\)
\(9 = \frac{ 99 }{ 5 + 6 }\)
\(10 = 69 - 59 \)
\(11 = \sqrt{6! - 599 }\)
\(12 = \frac{ 69 - 9 }{ 5 }\)
\(13 = 6 - 5 + \sqrt{9} + 9 \)
\(14 = 6 \cdot \sqrt{9} + 5 - 9 \)
\(15 = 95 - \frac{ 6! }{ 9 }\)
\(16 = 9 \cdot 9 - 65 \)
\(17 = \sqrt{69 - 5} + 9 \)
\(18 = \frac{ 69 }{ \sqrt{9} } - 5 \)
\(19 = 6 - 5 + 9 + 9 \)
\(20 = \frac{ 5! }{ 6 } - 9 + 9 \)
\(21 = \frac{ 96 + 9 }{ 5 }\)
\(22 = ( 9 - 6 ) \cdot 9 - 5 \)
\(23 = 59 - 6 \cdot \sqrt{9 }!\)
\(24 = 69 - 5 \cdot 9 \)
\(25 = 9 \cdot 9 - 56 \)
\(26 = 95 - 69 \)
\(27 = \frac{ 96 }{ \sqrt{9} } - 5 \)
\(28 = \frac{ 69 }{ \sqrt{9} } + 5 \)
\(29 = 56 - \sqrt{9} \cdot 9 \)
\(30 = 5 \cdot 6 - 9 + 9 \)
\(31 = 5 \cdot 6 + \frac{ 9 }{ 9 }\)
\(32 = ( 9 - 6 ) \cdot 9 + 5 \)
\(33 = \sqrt{969 + 5 !}\)
\(34 = 99 - 65 \)
\(35 = ( \frac{ 9 }{ 9 } + 6 ) \cdot 5 \)
\(36 = ( \frac{ 9 }{ 9 } + 5 ) \cdot 6 \)
\(37 = 96 - 59 \)
\(38 = 56 - 9 - 9 \)
\(39 = 69 - 5 \cdot \sqrt{9 }!\)
\(40 = 6 \cdot 9 - 5 - 9 \)
\(41 = 95 - 6 \cdot 9 \)
\(42 = 5! - 69 - 9 \)
\(43 = 99 - 56 \)
\(44 = 59 - 6 - 9 \)
\(45 = 69 - ( 9 - 5 )!\)
\(46 = 6 \cdot 9 - 5 - \sqrt{9 }\)
\(47 = 65 - 9 - 9 \)
\(48 = \frac{ 96 }{ 5 - \sqrt{9 } }\)
\(49 = \frac{ 5! }{ 9 - 6 } + 9 \)
\(50 = 56 - 9 + \sqrt{9 }\)
\(51 = 96 - 5 \cdot 9 \)
\(52 = 6 \cdot 9 - 5 + \sqrt{9 }\)
\(53 = 56 - \frac{ 9 }{ \sqrt{9 } }\)
\(54 = 69 - 5 \cdot \sqrt{9 }\)
\(55 = 56 - \frac{ 9 }{ 9 }\)
\(56 = 56 - 9 + 9 \)
\(57 = \frac{ 9 }{ 9 } + 56 \)
\(58 = 6 \cdot 9 - 5 + 9 \)
\(59 = \frac{ 9 }{ \sqrt{9} } + 56 \)
\(60 = 5! - 69 + 9 \)
\(61 = \frac{ 6 }{ \sqrt{9} } + 59 \)
\(62 = 59 - 6 + 9 \)
\(63 = \frac{ 69 + 5! }{ \sqrt{9 } }\)
\(64 = 65 - \frac{ 9 }{ 9 }\)
\(65 = 65 - 9 + 9 \)
\(66 = \frac{ 9 }{ 9 } + 65 \)
\(67 = 69 - 5 + \sqrt{9 }\)
\(68 = 56 + \sqrt{9} + 9 \)
\(69 = 99 - 5 \cdot 6 \)
\(70 = 9 \cdot 9 - 5 - 6 \)
\(71 = 65 - \sqrt{9} + 9 \)
\(72 = \sqrt{69 - 5} \cdot 9 \)
\(73 = 69 - 5 + 9 \)
\(74 = 56 + 9 + 9 \)
\(75 = ( 5 + 9 ) \cdot 6 - 9 \)
\(76 = \frac{ 6! }{ 9 } + 5 - 9 \)
\(77 = 6 \cdot \sqrt{9} + 59 \)
\(78 = ( 9 - 5 + 9 ) \cdot 6 \)
\(79 = 99 - \frac{ 5! }{ 6 }\)
\(80 = 95 - 6 - 9 \)
\(81 = 96 - 5 \cdot \sqrt{9 }\)
\(82 = 96 - 5 - 9 \)
\(83 = 65 + 9 + 9 \)
\(84 = 5 \cdot \sqrt{9} + 69 \)
\(85 = 96 - 5 - \sqrt{9 }!\)
\(86 = 95 - 6 - \sqrt{9 }\)
\(87 = 69 \cdot \sqrt{9} - 5 !\)
\(88 = 99 - 5 - 6 \)
\(89 = 95 - ( 9 - 6 )!\)
\(90 = ( 6 - 5 + 9 ) \cdot 9 \)
\(91 = 6^{\sqrt{9}} - 5^{\sqrt{9 }}\)
\(92 = 95 + 6 - 9 \)
\(93 = ( 9 - 5 )! + 69 \)
\(94 = 96 - 5 + \sqrt{9 }\)
\(95 = 6 \cdot \sqrt{9}! + 59 \)
\(96 = \frac{ \frac{ 6^{5} }{ 9 } }{ 9 }\)
\(97 = \frac{ 6 }{ \sqrt{9} } + 95 \)
\(98 = 95 - 6 + 9 \)
\(99 = ( 6 - 5 ) \cdot 99 \)
\(100 = 96 - 5 + 9 \)