Đáp án:
\(\begin{array}{l}
a)\sqrt 5 - 2\\
c)2\\
e)\dfrac{{13 - \sqrt 5 }}{2}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\sqrt {5 - 2.2.\sqrt 5 + 4} \\
= \sqrt {{{\left( {\sqrt 5 - 2} \right)}^2}} \\
= \sqrt 5 - 2\\
c)\sqrt {4 + \sqrt 8 } .\sqrt {\left( {2 + \sqrt {2 + \sqrt 2 } } \right)\left( {2 - \sqrt {2 + \sqrt 2 } } \right)} \\
= \sqrt {4 + \sqrt 8 } .\sqrt {4 - \left( {2 + \sqrt 2 } \right)} \\
= \sqrt {4 + \sqrt 8 } .\sqrt {2 - \sqrt 2 } \\
= \sqrt {2\left( {2 + \sqrt 2 } \right)\left( {2 - \sqrt 2 } \right)} \\
= \sqrt {2\left( {4 - 2} \right)} \\
= \sqrt {2.2} = 2\\
e)\dfrac{{{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2} + {{\left( {\sqrt 5 + \sqrt 3 } \right)}^2}}}{{\left( {\sqrt 5 - \sqrt 3 } \right)\left( {\sqrt 5 + \sqrt 3 } \right)}} - \dfrac{{{{\left( {\sqrt 5 + 1} \right)}^2}}}{{\left( {\sqrt 5 - 1} \right)\left( {\sqrt 5 + 1} \right)}}\\
= \dfrac{{8 - 2\sqrt {15} + 8 + 2\sqrt {15} }}{{5 - 3}} - \dfrac{{6 + 2\sqrt 5 }}{{5 - 1}}\\
= \dfrac{{16}}{2} - \dfrac{{6 + 2\sqrt 5 }}{4}\\
= 8 - \dfrac{{3 + \sqrt 5 }}{2}\\
= \dfrac{{16 - 3 - \sqrt 5 }}{2}\\
= \dfrac{{13 - \sqrt 5 }}{2}
\end{array}\)
