Đáp án:
\(\begin{array}{l}
a,\,\, - 6\sqrt 5 \\
b,\,\,\,4\\
c,\,\,\, - 7
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\dfrac{2}{{15}}\sqrt {45} - \sqrt {245} + \dfrac{{\sqrt {35} }}{{\sqrt 7 }} - \sqrt {\dfrac{4}{5}} \\
= \dfrac{2}{{15}}.\sqrt {9.5} - \sqrt {49.5} + \sqrt {\dfrac{{35}}{7}} - \sqrt {\dfrac{4}{{25}}.5} \\
= \dfrac{2}{{15}}\sqrt {{3^2}.5} - \sqrt {{7^2}.5} + \sqrt 5 - \sqrt {{{\left( {\dfrac{2}{5}} \right)}^2}.5} \\
= \dfrac{2}{{15}}.3\sqrt 5 - 7\sqrt 5 + \sqrt 5 - \dfrac{2}{5}\sqrt 5 \\
= \dfrac{2}{5}\sqrt 5 - 7\sqrt 5 + \sqrt 5 - \dfrac{2}{5}\sqrt 5 \\
= - 6\sqrt 5 \\
b,\\
\left( {\sqrt {14} - \sqrt 6 } \right).\sqrt {5 + \sqrt {21} } \\
= \left( {\sqrt 2 .\sqrt 7 - \sqrt 2 .\sqrt 3 } \right).\sqrt {5 + \sqrt {21} } \\
= \sqrt 2 .\left( {\sqrt 7 - \sqrt 3 } \right).\sqrt {5 + \sqrt {21} } \\
= \left( {\sqrt 7 - \sqrt 3 } \right).\sqrt {2.\left( {5 + \sqrt {21} } \right)} \\
= \left( {\sqrt 7 - \sqrt 3 } \right).\sqrt {10 + 2\sqrt {21} } \\
= \left( {\sqrt 7 - \sqrt 3 } \right).\sqrt {7 + 2.\sqrt 7 .\sqrt 3 + 3} \\
= \left( {\sqrt 7 - \sqrt 3 } \right).\sqrt {{{\left( {\sqrt 7 + \sqrt 3 } \right)}^2}} \\
= \left( {\sqrt 7 - \sqrt 3 } \right).\left| {\sqrt 7 + \sqrt 3 } \right|\\
= \left( {\sqrt 7 - \sqrt 3 } \right).\left( {\sqrt 7 + \sqrt 3 } \right)\\
= {\sqrt 7 ^2} - {\sqrt 3 ^2}\\
= 4\\
c,\\
2\sqrt {\dfrac{2}{{3 + \sqrt 5 }}} - \dfrac{{5\sqrt 5 - 1}}{{\sqrt 5 - 1}}\\
= 2\sqrt {\dfrac{{2\left( {3 - \sqrt 5 } \right)}}{{\left( {3 + \sqrt 5 } \right)\left( {3 - \sqrt 5 } \right)}}} - \dfrac{{\left( {5\sqrt 5 - 1} \right)\left( {\sqrt 5 + 1} \right)}}{{\left( {\sqrt 5 - 1} \right)\left( {\sqrt 5 + 1} \right)}}\\
= 2\sqrt {\dfrac{{6 - 2\sqrt 5 }}{{{3^2} - {{\sqrt 5 }^2}}}} - \dfrac{{5.{{\sqrt 5 }^2} + 5\sqrt 5 - \sqrt 5 - 1}}{{{{\sqrt 5 }^2} - {1^2}}}\\
= 2\sqrt {\dfrac{{5 - 2.\sqrt 5 .1 + 1}}{{9 - 5}}} - \dfrac{{5.5 + 4\sqrt 5 - 1}}{{5 - 1}}\\
= 2.\sqrt {\dfrac{{{{\left( {\sqrt 5 - 1} \right)}^2}}}{4}} - \dfrac{{24 + 4\sqrt 5 }}{4}\\
= 2.\dfrac{{\left| {\sqrt 5 - 1} \right|}}{2} - \left( {6 + \sqrt 5 } \right)\\
= \left( {\sqrt 5 - 1} \right) - \left( {6 + \sqrt 5 } \right)\\
= \sqrt 5 - 1 - 6 - \sqrt 5 \\
= - 7
\end{array}\)
