Đáp án:
\(\begin{array}{l}
B2:\\
a)3 + \sqrt 5 \\
b)\sqrt 5 - \sqrt 3 \\
c)3\sqrt 2 - 1\\
d)2\sqrt 6 - 3\\
B3:\\
a) - 1\\
b) - 2
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
B1:\\
A = \dfrac{{\sqrt {3.3} + \sqrt {5.5} }}{{\sqrt {3.5} }} = \dfrac{{3 + 5}}{{\sqrt {15} }}\\
= \dfrac{8}{{\sqrt {15} }}\\
B = \dfrac{{\sqrt {6 - 2\sqrt 5 } }}{{\sqrt 2 }}:\sqrt 2 \\
= \dfrac{{\sqrt {5 - 2\sqrt 5 .1 + 1} }}{{\sqrt {2.2} }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} }}{2}\\
= \dfrac{{\sqrt 5 - 1}}{2}\\
C = \sqrt {\dfrac{{2x - 2\sqrt {2x - 1} }}{{2x + 2\sqrt {2x - 1} }}} + \sqrt {\dfrac{{2x + 2\sqrt {2x - 1} }}{{2x - 2\sqrt {2x - 1} }}} \\
= \sqrt {\dfrac{{2x - 1 - 2\sqrt {2x - 1} .1 + 1}}{{2x - 1 + 2\sqrt {2x - 1} .1 + 1}}} + \sqrt {\dfrac{{2x - 1 + 2\sqrt {2x - 1} .1 + 1}}{{2x - 1 - 2\sqrt {2x - 1} .1 + 1}}} \\
= \sqrt {\dfrac{{{{\left( {\sqrt {2x - 1} - 1} \right)}^2}}}{{{{\left( {\sqrt {2x - 1} + 1} \right)}^2}}}} + \sqrt {\dfrac{{{{\left( {\sqrt {2x - 1} + 1} \right)}^2}}}{{{{\left( {\sqrt {2x - 1} - 1} \right)}^2}}}} \\
= \dfrac{{\sqrt {2x - 1} - 1}}{{\sqrt {2x - 1} + 1}} + \dfrac{{\sqrt {2x - 1} + 1}}{{\sqrt {2x - 1} - 1}}\\
= \dfrac{{{{\left( {\sqrt {2x - 1} - 1} \right)}^2} + {{\left( {\sqrt {2x - 1} + 1} \right)}^2}}}{{2x - 1 - 1}}\\
= \dfrac{{2x - 1 - 2\sqrt {2x - 1} + 1 + 2x - 1 + 2\sqrt {2x - 1} + 1}}{{2x - 2}}\\
= \dfrac{{4x}}{{2x - 2}} = \dfrac{{2x}}{{x - 1}}\\
B2:\\
a)\sqrt {9 + 2.3.\sqrt 5 + 5} = \sqrt {{{\left( {3 + \sqrt 5 } \right)}^2}} \\
= 3 + \sqrt 5 \\
b)\sqrt {5 - 2.\sqrt {5.3} + 3} = \sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} \\
= \sqrt 5 - \sqrt 3 \\
c)\sqrt {18 - 2.3\sqrt 2 .1 + 1} = \sqrt {{{\left( {3\sqrt 2 - 1} \right)}^2}} \\
= 3\sqrt 2 - 1\\
d)\sqrt {24 - 2.2\sqrt 6 .3 + 9} \\
= \sqrt {{{\left( {2\sqrt 6 - 3} \right)}^2}} \\
= 2\sqrt 6 - 3\\
B3:\\
a)\sqrt {22 - 12\sqrt 2 } - \sqrt {19 - 6\sqrt 2 } \\
= \sqrt {18 - 2.3\sqrt 2 .2 + 4} - \sqrt {18 - 2.3\sqrt 2 .1 + 1} \\
= \sqrt {{{\left( {3\sqrt 2 - 2} \right)}^2}} - \sqrt {{{\left( {3\sqrt 2 - 1} \right)}^2}} \\
= 3\sqrt 2 - 2 - \left( {3\sqrt 2 - 1} \right)\\
= - 1\\
b)\sqrt {24 - 2.2\sqrt 6 .3 + 9} - \sqrt {24 - 2.2\sqrt 6 .1 + 1} \\
= \sqrt {{{\left( {2\sqrt 6 - 3} \right)}^2}} - \sqrt {{{\left( {2\sqrt 6 - 1} \right)}^2}} \\
= 2\sqrt 6 - 3 - \left( {2\sqrt 6 - 1} \right)\\
= - 2
\end{array}\)
