All 100 targets have a solution.
\(1 = 91 - 90 \)
\(2 = 99^{0} + 1 \)
\(3 = ( 10 - 9 ) \cdot \sqrt{9 }\)
\(4 = 10 - 9 + \sqrt{9 }\)
\(5 = \sqrt{9}! - ( 10 - 9 )\)
\(6 = ( ( 10 - 9 ) \cdot \sqrt{9 } )!\)
\(7 = 10 - \frac{ 9 }{ \sqrt{9 } }\)
\(8 = 9 - ( 10 - 9 )\)
\(9 = ( 10 - 9 ) \cdot 9 \)
\(10 = \sqrt{109 - 9 }\)
\(11 = \frac{ 9 }{ 9 } + 10 \)
\(12 = 0 \cdot 1 + \sqrt{9} + 9 \)
\(13 = \frac{ 9 }{ \sqrt{9} } + 10 \)
\(14 = \sqrt{190 + \sqrt{9 }!}\)
\(15 = \frac{ 10 \cdot 9 }{ \sqrt{9 }! }\)
\(16 = 10 - \sqrt{9} + 9 \)
\(17 = \sqrt{9} \cdot 9 - 10 \)
\(18 = 19 - 9^{0 }\)
\(19 = 0 \cdot 9 + 19 \)
\(20 = 9^{0} + 19 \)
\(21 = 10 \cdot \sqrt{9} - 9 \)
\(22 = 10 + \sqrt{9} + 9 \)
\(23 = 19 + 0! + \sqrt{9 }\)
\(24 = ( 10 - 9 + \sqrt{9 } )!\)
\(25 = 10 + \sqrt{9}! + 9 \)
\(26 = ( 0 + \sqrt{9} ) \cdot 9 - 1 \)
\(27 = 19 - 0! + 9 \)
\(28 = 10 + 9 + 9 \)
\(29 = 19 + 0! + 9 \)
\(30 = \frac{ 10 \cdot 9 }{ \sqrt{9 } }\)
\(31 = \frac{ 90 }{ \sqrt{9} } + 1 \)
\(32 = ( 0! + \sqrt{9} ) \cdot ( 9 - 1 )\)
\(33 = 10 \cdot \sqrt{9} + \sqrt{9 }\)
\(34 = ( 0! + \sqrt{9} )! + 1 + 9 \)
\(35 = ( 0! + \sqrt{9} ) \cdot 9 - 1 \)
\(36 = ( 10 - \sqrt{9}! ) \cdot 9 \)
\(37 = \sqrt{9} \cdot 9 + 10 \)
\(38 = ( \sqrt{9} - 0! ) \cdot 19 \)
\(39 = 10 \cdot \sqrt{9} + 9 \)
\(40 = ( 0! + \sqrt{9} ) \cdot ( 1 + 9 )\)
\(41 = \frac{ ( \sqrt{9}! - 0! )! }{ \sqrt{9} } + 1 \)
\(42 = ( 10 - \sqrt{9} ) \cdot \sqrt{9 }!\)
\(43 = ( 0! + \sqrt{9} )! + 19 \)
\(44 = \sqrt{9}! \cdot 9 - 10 \)
\(45 = \frac{ 90 }{ \sqrt{9} - 1 }\)
\(46 = \sqrt{9}! \cdot \sqrt{9}! + 10 \)
\(47 = ( 9 - 0! ) \cdot \sqrt{9}! - 1 \)
\(48 = ( 10 + \sqrt{9}! ) \cdot \sqrt{9 }\)
\(49 = ( 9 - 0! ) \cdot \sqrt{9}! + 1 \)
\(50 = ( \sqrt{9}! - 0! ) \cdot ( 1 + 9 )\)
\(51 = 10 \cdot \sqrt{9}! - 9 \)
\(52 = \sqrt{9}! \cdot 9 - 0! - 1 \)
\(53 = ( 0 + \sqrt{9} )! \cdot 9 - 1 \)
\(54 = ( 19 - 0! ) \cdot \sqrt{9 }\)
\(55 = ( 0 + \sqrt{9} )! \cdot 9 + 1 \)
\(56 = 19 \cdot \sqrt{9} - 0 !\)
\(57 = ( 10 + 9 ) \cdot \sqrt{9 }\)
\(58 = 19 \cdot \sqrt{9} + 0 !\)
\(59 = ( 0! + 9 ) \cdot \sqrt{9}! - 1 \)
\(60 = ( 9 - \sqrt{9} ) \cdot 10 \)
\(61 = ( 0! + 9 ) \cdot \sqrt{9}! + 1 \)
\(62 = ( 0! + \sqrt{9}! ) \cdot 9 - 1 \)
\(63 = ( 10 - \sqrt{9} ) \cdot 9 \)
\(64 = \sqrt{9}! \cdot 9 + 10 \)
\(65 = ( 0! + \sqrt{9} )^{\sqrt{9}} + 1 \)
\(66 = 90 - ( 1 + \sqrt{9 } )!\)
\(67 = 91 - ( 0! + \sqrt{9 } )!\)
\(68 = \sqrt{( 0! + \sqrt{9}! )! + 1} - \sqrt{9 }\)
\(69 = 10 \cdot \sqrt{9}! + 9 \)
\(70 = \frac{ \sqrt{9}!! }{ 9 } - 10 \)
\(71 = 90 - 19 \)
\(72 = ( 9 - ( 0 + 1 ) ) \cdot 9 \)
\(73 = ( 9 - 0! ) \cdot 9 + 1 \)
\(74 = \sqrt{( 0! + \sqrt{9}! )! + 1} + \sqrt{9 }\)
\(75 = \frac{ \sqrt{9}!! }{ 10 } + \sqrt{9 }\)
\(76 = ( 0! + \sqrt{9} ) \cdot 19 \)
\(77 = \sqrt{( 0! + \sqrt{9}! )! + 1} + \sqrt{9 }!\)
\(78 = ( 10 + \sqrt{9} ) \cdot \sqrt{9 }!\)
\(79 = 9 \cdot 9 - 0! - 1 \)
\(80 = 90 - 1 - 9 \)
\(81 = 10 \cdot 9 - 9 \)
\(82 = 90 + 1 - 9 \)
\(83 = 91 + 0! - 9 \)
\(84 = 10 \cdot 9 - \sqrt{9 }!\)
\(85 = 90 + 1 - \sqrt{9 }!\)
\(86 = 90 - 1 - \sqrt{9 }\)
\(87 = 10 \cdot 9 - \sqrt{9 }\)
\(88 = 90 + 1 - \sqrt{9 }\)
\(89 = 99 - 10 \)
\(90 = 1^{9} \cdot 90 \)
\(91 = 9 \cdot 9 + 10 \)
\(92 = 9^{0} + 91 \)
\(93 = 10 \cdot 9 + \sqrt{9 }\)
\(94 = 90 + 1 + \sqrt{9 }\)
\(95 = 90 - 1 + \sqrt{9 }!\)
\(96 = 10 \cdot 9 + \sqrt{9 }!\)
\(97 = 99 - 0! - 1 \)
\(98 = 90 - 1 + 9 \)
\(99 = 10 \cdot 9 + 9 \)
\(100 = 109 - 9 \)