Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
\left( {\sqrt 3 + \sqrt 2 + 1} \right)\left( {\sqrt 3 + \sqrt 2 - 1} \right)\\
= {\left( {\sqrt 3 + \sqrt 2 } \right)^2} - {1^2}\\
= \left( {3 + 2.\sqrt 3 .\sqrt 2 + 2} \right) - 1\\
= 5 + 2\sqrt 6 - 1\\
= 4 + 2\sqrt 6 \\
2,\\
\left( {\sqrt 6 - \sqrt 5 + \sqrt 2 } \right)\left( {\sqrt 6 + \sqrt 5 - \sqrt 2 } \right)\\
= \left[ {\sqrt 6 - \left( {\sqrt 5 - \sqrt 2 } \right)} \right].\left[ {\sqrt 6 + \left( {\sqrt 5 - \sqrt 2 } \right)} \right]\\
= {\sqrt 6 ^2} - {\left( {\sqrt 5 - \sqrt 2 } \right)^2}\\
= 6 - \left( {5 - 2.\sqrt 5 .\sqrt 2 + 2} \right)\\
= 6 - \left( {7 - 2\sqrt {10} } \right)\\
= 6 - 7 + 2\sqrt {10} \\
= 2\sqrt {10} - 1\\
3,\\
\left( {2\sqrt {28} - 3\sqrt 7 + \sqrt {172} } \right).\sqrt {112} \\
= \left( {2.\sqrt {{2^2}.7} - 3\sqrt 7 + \sqrt {{2^2}.43} } \right).\sqrt {{4^2}.7} \\
= \left( {2.2\sqrt 7 - 3\sqrt 7 + 2\sqrt {43} } \right).4\sqrt 7 \\
= \left( {\sqrt 7 + 2\sqrt {43} } \right).4\sqrt 7 \\
= \sqrt 7 .4\sqrt 7 + 2.\sqrt {43} .4\sqrt 7 \\
= 28 + 8\sqrt {301} \\
4,\\
\left( {\sqrt 3 - 2\sqrt {12} + 2\sqrt 4 } \right).\left( {\sqrt {27} + \sqrt {144} - 2\sqrt {16} } \right)\\
= \left( {\sqrt 3 - 2.\sqrt {{2^2}.3} + 2.\sqrt {{2^2}} } \right)\left( {\sqrt {{3^2}.3} + \sqrt {{{12}^2}} - 2.\sqrt {{4^2}} } \right)\\
= \left( {\sqrt 3 - 2.2\sqrt 3 + 2.2} \right).\left( {3\sqrt 3 + 12 - 2.4} \right)\\
= \left( { - 3\sqrt 3 + 4} \right).\left( {3\sqrt 3 + 4} \right)\\
= {4^2} - {\left( {3\sqrt 3 } \right)^2}\\
= 16 - 27\\
= - 11
\end{array}\)
