Mọi người giúp với ạ

Mọi người giúp với ạ

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  1. Đáp án:

    Giải thích các bước giải:

    \(\begin{array}{l}
    1)\,\left( {5 + 2\sqrt 6 } \right)\left( {49 – 20\sqrt 6 } \right).\sqrt {5 – 2\sqrt 6 } \\
    = \left( {5 + 2\sqrt 6 } \right)\left( {25 – 2.5.2\sqrt 6 + 24} \right).\sqrt {{{\left( {\sqrt 3 – \sqrt 2 } \right)}^2}} \\
    = \left( {5 + 2\sqrt 6 } \right){\left( {5 – 2\sqrt 6 } \right)^2}\left( {\sqrt 3 – \sqrt 2 } \right)\\
    = \left( {5 + 2\sqrt 6 } \right)\left( {5 – 2\sqrt 6 } \right)\left( {5 – 2\sqrt 6 } \right)\left( {\sqrt 3 – \sqrt 2 } \right)\\
    = \left( {5 – 2\sqrt 6 } \right)\left( {\sqrt 3 – \sqrt 2 } \right)\\
    = 5\sqrt 3 – 5\sqrt 2 – 6\sqrt 2 + 4\sqrt 3 \\
    = 9\sqrt 3 – 11\sqrt 2 \\
    2)\,\left( {12 – 2\sqrt {11} } \right)\left( {\sqrt {22} + \sqrt 2 } \right)\sqrt {6 + \sqrt {11} } \\
    = \left( {12 – 2\sqrt {11} } \right)\left( {\sqrt {11} + 1} \right)\sqrt 2 \sqrt {6 + \sqrt {11} } \\
    = \left( {12 – 2\sqrt {11} } \right)\left( {\sqrt {11} + 1} \right)\sqrt {12 + 2\sqrt {11} } \\
    = \left( {12 – 2\sqrt {11} } \right)\left( {\sqrt {11} + 1} \right)\sqrt {{{\left( {\sqrt {11} + 1} \right)}^2}} \\
    = \left( {12 – 2\sqrt {11} } \right){\left( {\sqrt {11} + 1} \right)^2}\\
    = {\left( {\sqrt {11} – 1} \right)^2}{\left( {\sqrt {11} + 1} \right)^2} = 100\\
    3)\,\sqrt {3 + \sqrt 5 } – \sqrt {3 – \sqrt 5 } – \sqrt 2 \\
    = \dfrac{1}{{\sqrt 2 }}\left( {\sqrt {6 + 2\sqrt 5 } – \sqrt {6 – 2\sqrt 5 } } \right) – \sqrt 2 \\
    = \dfrac{1}{{\sqrt 2 }}\left( {\sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} – \sqrt {{{\left( {\sqrt 5 – 1} \right)}^2}} } \right) – \sqrt 2 \\
    = \dfrac{1}{{\sqrt 2 }}\left( {\sqrt 5 + 1 – \sqrt 5 + 1} \right) – \sqrt 2 \\
    = \dfrac{1}{{\sqrt 2 }}.2 – \sqrt 2 = \sqrt 2 – \sqrt 2 = 0
    \end{array}\)

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