Đáp án:
\(\begin{array}{l}
a)7\\
b) - 2\\
c) - 7\\
d)\sqrt 5 + 2\\
e) - 2\sqrt 2
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left( {3 - \sqrt 2 } \right)\sqrt {11 + 6\sqrt 2 } \\
= \left( {3 - \sqrt 2 } \right)\sqrt {9 + 2.3.\sqrt 2 + 2} \\
= \left( {3 - \sqrt 2 } \right)\sqrt {{{\left( {3 + \sqrt 2 } \right)}^2}} \\
= \left( {3 - \sqrt 2 } \right)\left( {3 + \sqrt 2 } \right)\\
= 9 - 2 = 7\\
b)\left( {\sqrt 5 + \sqrt 7 } \right)\sqrt {12 - 2.\sqrt {35} } \\
= \left( {\sqrt 5 + \sqrt 7 } \right)\sqrt {7 - 2.\sqrt 7 .\sqrt 5 + 5} \\
= \left( {\sqrt 5 + \sqrt 7 } \right)\sqrt {{{\left( {\sqrt 5 - \sqrt 7 } \right)}^2}} \\
= \left( {\sqrt 5 + \sqrt 7 } \right)\left( {\sqrt 5 - \sqrt 7 } \right)\\
= 5 - 7 = - 2\\
c)\left( {\sqrt 2 - \sqrt 9 } \right)\sqrt {11 + 2\sqrt {18} } \\
= \left( {\sqrt 2 - \sqrt 9 } \right)\sqrt {\left( {9 + 2.\sqrt 9 .\sqrt 2 + 2} \right)} \\
= \left( {\sqrt 2 - \sqrt 9 } \right)\sqrt {{{\left( {\sqrt 9 + \sqrt 2 } \right)}^2}} \\
= \left( {\sqrt 2 - \sqrt 9 } \right)\left( {\sqrt 2 + \sqrt 9 } \right)\\
= 2 - 9 = - 7\\
d)\sqrt {46 - 6\sqrt 5 } - \sqrt {29 - 12\sqrt 5 } \\
= \sqrt {45 - 2.3\sqrt 5 .1 + 1} - \sqrt {20 - 2.2\sqrt 5 .3 + 9} \\
= \sqrt {{{\left( {3\sqrt 5 - 1} \right)}^2}} - \sqrt {{{\left( {2\sqrt 5 - 3} \right)}^2}} \\
= 3\sqrt 5 - 1 - \left( {2\sqrt 5 - 3} \right)\\
= \sqrt 5 + 2\\
e)\sqrt {7 - 2\sqrt {10} } - \sqrt {7 + 2\sqrt {10} } \\
= \sqrt {5 - 2.\sqrt 5 .\sqrt 2 + 2} - \sqrt {5 + 2.\sqrt 5 .\sqrt 2 + 2} \\
= \sqrt {{{\left( {\sqrt 5 - \sqrt 2 } \right)}^2}} - \sqrt {{{\left( {\sqrt 5 + \sqrt 2 } \right)}^2}} \\
= \sqrt 5 - \sqrt 2 - \sqrt 5 - \sqrt 2 \\
= - 2\sqrt 2
\end{array}\)
