Đáp án:
$\begin{array}{l}
4)\sqrt {49 - 20\sqrt 6 } \\
= \sqrt {25 - 2.5.2.\sqrt 6 + 24} \\
= \sqrt {{{\left( {5 - 2\sqrt 6 } \right)}^2}} \\
= 5 - 2\sqrt 6 \\
5)\sqrt {36 + 12\sqrt 5 } \\
= \sqrt {30 + 2.6.\sqrt 5 + 6} \\
= \sqrt {30 + 2.\sqrt {30} .\sqrt 6 + 6} \\
= \sqrt {{{\left( {\sqrt {30} + \sqrt 6 } \right)}^2}} \\
= \sqrt {30} + \sqrt 6 \\
6)\sqrt {23 - 4\sqrt {15} } \\
= \sqrt {23 - 2.2.\sqrt 5 .\sqrt 3 } \\
= \sqrt {20 - 2.2\sqrt 5 .\sqrt 3 + 3} \\
= \sqrt {{{\left( {2\sqrt 5 - \sqrt 3 } \right)}^2}} \\
= 2\sqrt 5 - \sqrt 3 \\
7)\sqrt {23 + 6\sqrt {10} } \\
= \sqrt {18 + 2.3.\sqrt 2 .\sqrt 5 + 5} \\
= \sqrt {{{\left( {3\sqrt 2 + \sqrt 5 } \right)}^2}} \\
= 3\sqrt 2 + \sqrt 5 \\
8)\sqrt {11 + 4\sqrt 7 } \\
= \sqrt {7 + 2.2.\sqrt 7 + 4} \\
= \sqrt {{{\left( {\sqrt 7 + 2} \right)}^2}} \\
= \sqrt 7 + 2
\end{array}$
