Đáp án:
\(\begin{array}{l}
A = 30\\
C = \sqrt 2 + 1\\
E = 18\\
B = 2\sqrt 3 \\
D = 3\sqrt 5 - 1\\
F = \sqrt {10}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
A = 3.2.5 + 6 + 5 + \sqrt {{2^8}} - 3.9\\
= 30 + 11 + {2^4} - 27\\
= 30\\
C = \sqrt {2 + 2.\sqrt 2 .1 + 1} \\
= \sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}} = \sqrt 2 + 1\\
E = \left| {1 - \sqrt 5 } \right| + \left| {3 - \sqrt 5 } \right| + {2.2^3}\\
= - 1 + \sqrt 5 + 3 - \sqrt 5 + 16\\
= 18\\
B = \sqrt {4 + 2.2.\sqrt 3 + 3} - \sqrt {4 - 2.2.\sqrt 3 + 3} \\
= \sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} - \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} \\
= 2 + \sqrt 3 - 2 + \sqrt 3 = 2\sqrt 3 \\
D = \sqrt {5 + 2.\sqrt 5 .1 + 1} + 2\sqrt {5 - 2.\sqrt 5 .1 + 1} \\
= \sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} + 2\sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} \\
= \sqrt 5 + 1 + 2\left( {\sqrt 5 - 1} \right)\\
= 3\sqrt 5 - 1\\
F = \sqrt {3 + \sqrt 5 } + \sqrt {3 - \sqrt 5 } \\
= \dfrac{{\sqrt {6 + 2\sqrt 5 } }}{{\sqrt 2 }} + \dfrac{{\sqrt {6 - 2\sqrt 5 } }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {5 + 2.\sqrt 5 .1 + 1} }}{{\sqrt 2 }} + \dfrac{{\sqrt {5 - 2.\sqrt 5 .1 + 1} }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} }}{{\sqrt 2 }} + \dfrac{{\sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt 5 + 1 + \sqrt 5 - 1}}{{\sqrt 2 }}\\
= \dfrac{{2\sqrt 5 }}{{\sqrt 2 }} = \sqrt {10}
\end{array}\)
