Đáp án:
\(\begin{array}{l}
d)8\\
e)2\sqrt 5 \\
f)3\sqrt 5
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
d)D = \sqrt {3 - \sqrt 5 } .\left( {3 + \sqrt 5 } \right).\sqrt 2 \left( {\sqrt 5 - 1} \right)\\
= \sqrt {6 - 2\sqrt 5 } .\left( {3 + \sqrt 5 } \right)\left( {\sqrt 5 - 1} \right)\\
= \sqrt {5 - 2.\sqrt 5 .1 + 1} .\left( {3 + \sqrt 5 } \right)\left( {\sqrt 5 - 1} \right)\\
= \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} .\left( {3 + \sqrt 5 } \right)\left( {\sqrt 5 - 1} \right)\\
= \left( {\sqrt 5 - 1} \right)\left( {3 + \sqrt 5 } \right)\left( {\sqrt 5 - 1} \right)\\
= \left( {5 - 2\sqrt 5 + 1} \right)\left( {3 + \sqrt 5 } \right)\\
= 2\left( {3 - \sqrt 5 } \right)\left( {3 + \sqrt 5 } \right)\\
= 2.\left( {9 - 5} \right)\\
= 2.4 = 8\\
e)2\sqrt 3 + \dfrac{4}{{\sqrt 3 + \sqrt 5 }}\\
= 2\sqrt 3 + \dfrac{{4\left( {\sqrt 3 - \sqrt 5 } \right)}}{{3 - 5}}\\
= 2\sqrt 3 - 2\left( {\sqrt 3 - \sqrt 5 } \right)\\
= 2\sqrt 5 \\
f)\sqrt {5 - 2.\sqrt {5.2} + 2} + 2\sqrt 5 + \dfrac{1}{2}.2\sqrt 2 \\
= \sqrt {{{\left( {\sqrt 5 - \sqrt 2 } \right)}^2}} + 2\sqrt 5 + \sqrt 2 \\
= \sqrt 5 - \sqrt 2 + 2\sqrt 5 + \sqrt 2 \\
= 3\sqrt 5
\end{array}\)
