Đáp án:
\(\begin{array}{l}
B1:\\
b)2\\
c) - \sqrt 2 \\
B2:\\
3)3\\
4)2
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
B1:\\
b)\left( {\sqrt 5 + \sqrt 3 } \right)\sqrt {5 - 2.\sqrt 5 .\sqrt 3 + 3} \\
= \left( {\sqrt 5 + \sqrt 3 } \right)\sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} \\
= \left( {\sqrt 5 + \sqrt 3 } \right)\left( {\sqrt 5 - \sqrt 3 } \right)\\
= 5 - 3 = 2\\
c)\dfrac{{\sqrt {6 - 2\sqrt 5 } - \sqrt {6 + 2\sqrt 5 } }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {5 - 2\sqrt 5 .1 + 1} - \sqrt {5 + 2\sqrt 5 .1 + 1} }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} - \sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt 5 - 1 - \sqrt 5 - 1}}{{\sqrt 2 }}\\
= - \dfrac{2}{{\sqrt 2 }} = - \sqrt 2 \\
B2:\\
3)\sqrt {\left( {\sqrt {13} - 2} \right)\left( {\sqrt {13} + 2} \right)} \\
= \sqrt {{{\left( {\sqrt {13} } \right)}^2} - {2^2}} \\
= \sqrt {13 - 4} = \sqrt 9 = 3\\
4)\sqrt 2 \left( {\sqrt 3 + 1} \right)\sqrt {2 - \sqrt 3 } \\
= \left( {\sqrt 3 + 1} \right)\sqrt {4 - 2\sqrt 3 } \\
= \left( {\sqrt 3 + 1} \right)\sqrt {3 - 2\sqrt 3 .1 + 1} \\
= \left( {\sqrt 3 + 1} \right)\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} \\
= \left( {\sqrt 3 + 1} \right)\left( {\sqrt 3 - 1} \right)\\
= 3 - 1 = 2
\end{array}\)
