Đáp án:
$\begin{array}{l}
a)\sqrt {49 - 20\sqrt 6 } \\
= \sqrt {25 - 2.5.2\sqrt 6 + 24} \\
= \sqrt {{{\left( {5 - 2\sqrt 6 } \right)}^2}} \\
= 5 - 2\sqrt 6 \\
b)\sqrt {98 - 16\sqrt 3 } \\
= \sqrt {2.\left( {49 - 8\sqrt 3 } \right)} \\
= \sqrt 2 .\sqrt {48 - 2.4\sqrt 3 + 1} \\
= \sqrt 2 .\sqrt {{{\left( {4\sqrt 3 - 1} \right)}^2}} \\
= \sqrt 2 .\left( {4\sqrt 3 - 1} \right)\\
= 4\sqrt 6 - \sqrt 2 \\
c)\sqrt {33 + 20\sqrt 2 } \\
= \sqrt {25 + 2.5.2\sqrt 2 + 8} \\
= \sqrt {{{\left( {5 + 2\sqrt 2 } \right)}^2}} \\
= 5 + 2\sqrt 2 \\
d)\sqrt {5 - \sqrt {21} } \\
= \sqrt {\dfrac{{10 - 2\sqrt {21} }}{2}} \\
= \sqrt {{{\dfrac{{\left( {\sqrt 7 - \sqrt 3 } \right)}}{2}}^2}} \\
= \dfrac{1}{{\sqrt 2 }}.\left( {\sqrt 7 - \sqrt 3 } \right)\\
= \dfrac{{\sqrt {14} - \sqrt 6 }}{2}\\
e)\sqrt {2 - \sqrt 3 } \\
= \dfrac{{\sqrt {4 - 2\sqrt 3 } }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt 3 - 1}}{{\sqrt 2 }}\\
= \dfrac{{\sqrt 6 - \sqrt 2 }}{2}\\
f)\sqrt {36 + 12\sqrt 5 } \\
= \sqrt {6.\left( {6 + 2\sqrt 5 } \right)} \\
= \sqrt 6 .\sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} \\
= \sqrt 6 \left( {\sqrt 5 + 1} \right)\\
= \sqrt {30} + \sqrt 6 \\
g)\sqrt {4 + \sqrt {15} } + \sqrt {4 - \sqrt {15} } \\
= \dfrac{1}{{\sqrt 2 }}\left( {\sqrt {8 + 2\sqrt {15} } + \sqrt {8 - 2\sqrt {15} } } \right)\\
= \dfrac{{\sqrt 2 }}{2}.\left( {\sqrt {{{\left( {\sqrt 5 + \sqrt 3 } \right)}^2}} + \sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} } \right)\\
= \dfrac{{\sqrt 2 }}{2}.\left( {\sqrt 5 + \sqrt 3 + \sqrt 5 - \sqrt 3 } \right)\\
= \dfrac{{\sqrt 2 }}{2}.2\sqrt 5 \\
= \sqrt {10}
\end{array}$
