Đáp án:
\(\begin{array}{l}
c)6\\
f)4\\
i)12 - 4\sqrt 5 \\
l)2
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
c)2 + 2\sqrt 2 + 1 + 2 - 2\sqrt 2 + 1\\
= 6\\
f)\sqrt {4 + 2.2.\sqrt 3 + 3} + \sqrt {4 - 2.2.\sqrt 3 + 3} \\
= \sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} + \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} \\
= 2 + \sqrt 3 + 2 - \sqrt 3 \\
= 4\\
i)\left( {3 - \sqrt 5 } \right).\left( {\sqrt 5 - 1} \right).\sqrt 2 .\sqrt {3 + \sqrt 5 } \\
= \left( {3 - \sqrt 5 } \right).\left( {\sqrt 5 - 1} \right)\sqrt {6 + 2\sqrt 5 } \\
= \left( {3 - \sqrt 5 } \right).\left( {\sqrt 5 - 1} \right)\sqrt {5 + 2\sqrt 5 .1 + 1} \\
= \left( {3 - \sqrt 5 } \right).\left( {\sqrt 5 - 1} \right)\sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} \\
= \left( {3 - \sqrt 5 } \right).\left( {\sqrt 5 - 1} \right)\left( {\sqrt 5 + 1} \right)\\
= \left( {3 - \sqrt 5 } \right)\left( {5 - 1} \right)\\
= 4\left( {3 - \sqrt 5 } \right)\\
= 12 - 4\sqrt 5 \\
l)\left( {4 + \sqrt {15} } \right).\left( {\sqrt 5 - \sqrt 3 } \right).\sqrt 2 .\sqrt {4 - \sqrt {15} } \\
= \left( {4 + \sqrt {15} } \right).\left( {\sqrt 5 - \sqrt 3 } \right)\sqrt {8 - 2\sqrt {15} } \\
= \left( {4 + \sqrt {15} } \right).\left( {\sqrt 5 - \sqrt 3 } \right)\sqrt {5 - 2.\sqrt 5 .\sqrt 3 + 3} \\
= \left( {4 + \sqrt {15} } \right).\left( {\sqrt 5 - \sqrt 3 } \right)\sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} \\
= \left( {4 + \sqrt {15} } \right).{\left( {\sqrt 5 - \sqrt 3 } \right)^2}\\
= \left( {4 + \sqrt {15} } \right).\left( {8 - 2\sqrt {15} } \right)\\
= 2\left( {4 + \sqrt {15} } \right)\left( {4 - \sqrt {15} } \right)\\
= 2\left( {16 - 15} \right) = 2
\end{array}\)
