Đáp án:
\(\begin{array}{l}
4)4\\
5)2\\
6)4
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
4)\left( {\sqrt 3 + \sqrt 7 } \right).\sqrt 2 .\sqrt {5 - \sqrt {21} } \\
= \left( {\sqrt 3 + \sqrt 7 } \right)\sqrt {10 - 2\sqrt {21} } \\
= \left( {\sqrt 3 + \sqrt 7 } \right)\sqrt {7 - 2.\sqrt 7 .\sqrt 3 + 3} \\
= \left( {\sqrt 3 + \sqrt 7 } \right)\sqrt {{{\left( {\sqrt 7 - \sqrt 3 } \right)}^2}} \\
= \left( {\sqrt 7 - \sqrt 3 } \right)\left( {\sqrt 7 + \sqrt 3 } \right)\\
= 7 - 3 = 4\\
5)\sqrt {9 - 2.3.\sqrt 7 + 7} .\left( {3 + \sqrt 7 } \right)\\
= \sqrt {{{\left( {3 - \sqrt 7 } \right)}^2}} .\left( {3 + \sqrt 7 } \right)\\
= \left( {3 - \sqrt 7 } \right)\left( {3 + \sqrt 7 } \right)\\
= 9 - 7 = 2\\
6)\left( {\sqrt {8 + 3\sqrt 7 } - \sqrt {6 - 3\sqrt 3 } } \right).\sqrt 2 \left( {\sqrt 7 - \sqrt 3 } \right)\\
= \left( {\sqrt {16 + 6\sqrt 7 } - \sqrt {12 - 6\sqrt 3 } } \right)\left( {\sqrt 7 - \sqrt 3 } \right)\\
= \left( {\sqrt {9 + 2.3.\sqrt 7 + 7} - \sqrt {9 - 2.3.\sqrt 3 + 3} } \right).\left( {\sqrt 7 - \sqrt 3 } \right)\\
= \left( {\sqrt {{{\left( {3 + \sqrt 7 } \right)}^2}} - \sqrt {{{\left( {3 - \sqrt 3 } \right)}^2}} } \right)\left( {\sqrt 7 - \sqrt 3 } \right)\\
= \left( {3 + \sqrt 7 - 3 + \sqrt 3 } \right).\left( {\sqrt 7 - \sqrt 3 } \right)\\
= \left( {\sqrt 7 + \sqrt 3 } \right)\left( {\sqrt 7 - \sqrt 3 } \right)\\
= 7 - 3 = 4
\end{array}\)
