Đáp án:
\(\begin{array}{l}
b) - 8\sqrt 3 \\
d)2\sqrt 2 - 3\\
f)5
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
b)2\sqrt 3 + 4\sqrt 3 - 5\sqrt 3 - 9\sqrt 3 \\
= \left( {2 + 4 - 5 - 9} \right)\sqrt 3 \\
= - 8\sqrt 3 \\
d)\sqrt {2 - 2\sqrt 2 .1 + 1} - \sqrt {4 - 2.2.\sqrt 2 + 2} \\
= \sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}} - \sqrt {{{\left( {2 - \sqrt 2 } \right)}^2}} \\
= \sqrt 2 - 1 - \left( {2 - \sqrt 2 } \right)\\
= 2\sqrt 2 - 3\\
f)\sqrt {5\sqrt 3 + 5\sqrt {48 - 10\sqrt {4 + 2.2\sqrt 3 + 3} } } \\
= \sqrt {5\sqrt 3 + 5\sqrt {48 - 10\sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} } } \\
= \sqrt {5\sqrt 3 + 5\sqrt {48 - 10\left( {2 + \sqrt 3 } \right)} } \\
= \sqrt {5\sqrt 3 + 5\sqrt {28 - 10\sqrt 3 } } \\
= \sqrt {5\sqrt 3 + 5\sqrt {25 - 2.5\sqrt 3 + 3} } \\
= \sqrt {5\sqrt 3 + 5\sqrt {{{\left( {5 - \sqrt 3 } \right)}^2}} } \\
= \sqrt {5\sqrt 3 + 5\left( {5 - \sqrt 3 } \right)} \\
= \sqrt {5\sqrt 3 + 25 - 5\sqrt 3 } = 5
\end{array}\)
