Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
A = \left( {2 - \sqrt 3 } \right).\sqrt {7 + 4\sqrt 3 }  + \left( {2\sqrt 2  + 3} \right).\sqrt {17 - 3\sqrt {32} } \\
 = \left( {2 - \sqrt 3 } \right).\sqrt {4 + 2.2.\sqrt 3  + 3}  + \left( {2\sqrt 2  + 3} \right).\sqrt {8 + 9 - 3.\sqrt {{4^2}.2} } \\
 = \left( {2 - \sqrt 3 } \right).\sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}}  + \left( {2\sqrt 2  + 3} \right).\sqrt {{{\left( {2\sqrt 2 } \right)}^2} + 9 - 3.4.\sqrt 2 } \\
 = \left( {2 - \sqrt 3 } \right).\left( {2 + \sqrt 3 } \right) + \left( {2\sqrt 2  + 3} \right).\sqrt {{3^2} - 2.3.2\sqrt 2  + {{\left( {2\sqrt 2 } \right)}^2}} \\
 = \left( {{2^2} - {{\sqrt 3 }^2}} \right) + \left( {2\sqrt 2  + 3} \right).\sqrt {{{\left( {2\sqrt 2  - 3} \right)}^2}} \\
 = \left( {4 - 3} \right) + \left( {2\sqrt 2  + 3} \right).\left( {3 - 2\sqrt 2 } \right)\\
 = 1 + {3^2} - {\left( {2\sqrt 2 } \right)^2}\\
 = 1 + 1\\
 = 2\\
B = \left( {\sqrt 5  + 3} \right)\sqrt {14 - 6\sqrt 5 }  - \left( {3 + 2\sqrt 5 } \right)\sqrt {29 - 12\sqrt 5 } \\
 = \left( {\sqrt 5  + 3} \right).\sqrt {9 - 2.3.\sqrt 5  + 5}  - \left( {3 + 2\sqrt 5 } \right).\sqrt {20 - 2.2\sqrt 5 .3 + 9} \\
 = \left( {\sqrt 5  + 3} \right).\sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}}  - \left( {3 + 2\sqrt 5 } \right).\sqrt {{{\left( {2\sqrt 5 } \right)}^2} - 2.2\sqrt 5 .3 + {3^2}} \\
 = \left( {\sqrt 5  + 3} \right).\left( {3 - \sqrt 5 } \right) - \left( {3 + 2\sqrt 5 } \right).\sqrt {{{\left( {2\sqrt 5  - 3} \right)}^2}} \\
 = \left( {{3^2} - {{\sqrt 5 }^2}} \right) - \left( {3 + 2\sqrt 5 } \right).\left( {2\sqrt 5  - 3} \right)\\
 = \left( {9 - 5} \right) - \left( {{{\left( {2\sqrt 5 } \right)}^2} - {3^2}} \right)\\
 = 4 - 11\\
 =  - 7\\
C = \sqrt {4 - 2\sqrt 3 }  + \sqrt {7 - \sqrt {48} } \\
 = \sqrt {4 - 2\sqrt 3 }  + \sqrt {7 - \sqrt {{4^2}.3} } \\
 = \sqrt {4 - 2\sqrt 3 }  + \sqrt {7 - 4\sqrt 3 } \\
 = \sqrt {3 - 2.\sqrt 3 .1 + 1}  + \sqrt {4 - 2.2.\sqrt 3  + 3} \\
 = \sqrt {{{\left( {\sqrt 3  - 1} \right)}^2}}  + \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} \\
 = \left( {\sqrt 3  - 1} \right) + \left( {2 - \sqrt 3 } \right)\\
 = 1
\end{array}\)