Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\sqrt {8 - 2\sqrt {12} } + \sqrt 2 \\
= \sqrt {6 - 2.\sqrt 6 .\sqrt 2 + 2} + \sqrt 2 \\
= \sqrt {{{\left( {\sqrt 6 - \sqrt 2 } \right)}^2}} + \sqrt 2 \\
= \sqrt 6 - \sqrt 2 + \sqrt 2 \\
= \sqrt 6 \\
b,\\
\sqrt {12 + 2\sqrt {35} } - \sqrt {7 - 2\sqrt {10} } \\
= \sqrt {7 + 2.\sqrt 7 .\sqrt 5 + 5} - \sqrt {5 - 2.\sqrt 5 .\sqrt 2 + 2} \\
= \sqrt {{{\left( {\sqrt 7 + \sqrt 5 } \right)}^2}} - \sqrt {{{\left( {\sqrt 5 - \sqrt 2 } \right)}^2}} \\
= \left( {\sqrt 7 + \sqrt 5 } \right) - \left( {\sqrt 5 - \sqrt 2 } \right)\\
= \sqrt 7 + \sqrt 2 \\
c,\\
\sqrt {16 + 2\sqrt {55} } - \sqrt {11} \\
= \sqrt {11 + 2.\sqrt {11} .\sqrt 5 + 5} - \sqrt {11} \\
= \sqrt {{{\left( {\sqrt {11} + \sqrt 5 } \right)}^2}} - \sqrt {11} \\
= \left( {\sqrt {11} + \sqrt 5 } \right) - \sqrt {11} \\
= \sqrt 5 \\
d,\\
\sqrt {11 - 4\sqrt 6 } - 2\sqrt 2 \\
= \sqrt {8 - 2.2\sqrt 2 .\sqrt 3 + 3} - 2\sqrt 2 \\
= \sqrt {{{\left( {2\sqrt 2 - \sqrt 3 } \right)}^2}} - 2\sqrt 2 \\
= 2\sqrt 2 - \sqrt 3 - 2\sqrt 2 \\
= - \sqrt 3 \\
e,\\
\sqrt {\sqrt 3 - \sqrt {1 - \sqrt {21 - 12\sqrt 3 } } } \\
= \sqrt {\sqrt 3 - \sqrt {1 - \sqrt {12 - 2.2\sqrt 3 .3 + 9} } } \\
= \sqrt {\sqrt 3 - \sqrt {1 - \sqrt {{{\left( {2\sqrt 3 - 3} \right)}^2}} } } \\
= \sqrt {\sqrt 3 - \sqrt {1 - \left( {2\sqrt 3 - 3} \right)} } \\
= \sqrt {\sqrt 3 - \sqrt {4 - 2\sqrt 3 } } \\
= \sqrt {\sqrt 3 - \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} } \\
= \sqrt {\sqrt 3 - \left( {\sqrt 3 - 1} \right)} \\
= \sqrt 1 \\
= 1
\end{array}\)
