Đáp án:
\(\begin{array}{l}
a)\dfrac{{23\sqrt 2 }}{2} - \dfrac{{3\sqrt 6 }}{2}\\
b) - 2\sqrt 5 \\
c)13\\
d)2
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)2.5\sqrt 2 - 3.\dfrac{{\sqrt 2 }}{2} + 5.\sqrt {\dfrac{{45}}{{10}}} - 7.\sqrt {\dfrac{3}{2}} - 2\sqrt 2 + 2\sqrt 6 - \sqrt {\dfrac{{125}}{{10}}} \\
= 10\sqrt 2 - \dfrac{{3\sqrt 2 }}{2} + \dfrac{{15\sqrt 2 }}{2} - \dfrac{{7\sqrt 6 }}{2} - 2\sqrt 2 + 2\sqrt 6 - \dfrac{{5\sqrt 2 }}{2}\\
= \dfrac{{23\sqrt 2 }}{2} - \dfrac{{3\sqrt 6 }}{2}\\
b)\sqrt {5 - 2\sqrt 5 .1 + 1} - \left| {1 - 3\sqrt 5 } \right|\\
= \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} - \left( {3\sqrt 5 - 1} \right)\\
= \sqrt 5 - 1 - 3\sqrt 5 + 1\\
= - 2\sqrt 5 \\
c)\left( {\sqrt 3 + 4} \right).\sqrt {16 - 2.4.\sqrt 3 + 3} \\
= \left( {\sqrt 3 + 4} \right).\sqrt {{{\left( {4 - \sqrt 3 } \right)}^2}} \\
= \left( {\sqrt 3 + 4} \right).\left( {4 - \sqrt 3 } \right)\\
= 16 - 3 = 13\\
d)\dfrac{{\sqrt {2 - 2\sqrt 2 .1 + 1} }}{{\sqrt {9 - 2.3.2\sqrt 2 + 8} }} - \dfrac{{\sqrt {2 + 2\sqrt 2 .1 + 1} }}{{\sqrt {9 + 2.3.2\sqrt 2 + 8} }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}} }}{{\sqrt {{{\left( {3 - 2\sqrt 2 } \right)}^2}} }} - \dfrac{{\sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}} }}{{\sqrt {{{\left( {3 + 2\sqrt 2 } \right)}^2}} }}\\
= \dfrac{{\sqrt 2 - 1}}{{3 - 2\sqrt 2 }} - \dfrac{{\sqrt 2 + 1}}{{3 + 2\sqrt 2 }}\\
= \dfrac{{\left( {\sqrt 2 - 1} \right)\left( {3 + 2\sqrt 2 } \right) - \left( {\sqrt 2 + 1} \right)\left( {3 - 2\sqrt 2 } \right)}}{{9 - 8}}\\
= 3\sqrt 2 + 2.2 - 3 - 2\sqrt 2 - 3\sqrt 2 + 2.2 - 3 + 2\sqrt 2 \\
= 2
\end{array}\)
