Đáp án:
$\begin{array}{l}
B10:\\
a) - 8a\\
b) - 9{a^3}\\
c)2\sqrt 3 \\
d)0\\
B11:\\
a) - 4\sqrt 6 \\
b) - 4a\\
B12:\\
a)7a\\
b) - 2x
\end{array}$
Giải thích các bước giải:
$\begin{array}{l}
B10:\\
a)3\sqrt {{a^2}} - 5a\left( {DK:a \le 0} \right)\\
= 3\left| a \right| - 5a\\
= 3\left( { - a} \right) - 5a\\
= - 8a\\
b)3\sqrt {4{a^6}} - 3{a^3}\left( {DK:a \le 0} \right)\\
= 3\sqrt {{{\left( {2{a^3}} \right)}^2}} - 3{a^3}\\
= 3\left| {2{a^3}} \right| - 3{a^3}\\
= 3\left( { - 2{a^3}} \right) - 3{a^3}\\
= - 9{a^3}\\
c)\sqrt {4 + 2\sqrt 3 } + \sqrt {4 - 2\sqrt 3 } \\
= \sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} + \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} \\
= \left| {\sqrt 3 + 1} \right| + \left| {\sqrt 3 - 1} \right|\\
= \sqrt 3 + 1 + \sqrt 3 - 1\\
= 2\sqrt 3 \\
d)x - 2 - \sqrt {4 - 4x + {x^2}} \left( {DK:x > 2} \right)\\
= x - 2 - \sqrt {{{\left( {x - 2} \right)}^2}} \\
= x - 2 - \left| {x - 2} \right|\\
= x - 2 - \left( {x - 2} \right)\\
= 0\\
B11:\\
a)2\sqrt {24} - 2\sqrt {54} + 3\sqrt 6 - \sqrt {150} \\
= 2.2\sqrt 6 - 2.3\sqrt 6 + 3\sqrt 6 - 5\sqrt 6 \\
= - 4\sqrt 6 \\
b)5\sqrt {4a} - 4\sqrt {{a^2}} - \sqrt {100a} \left( {DK:a > 0} \right)\\
= 5.2\sqrt a - 4\left| a \right| - 10\sqrt a \\
= 10\sqrt a - 4a - 10\sqrt a \\
= - 4a\\
B12:\\
a)\sqrt {4{a^2}} + 5a\left( {DK:a \ge 0} \right)\\
= \sqrt {{{\left( {2a} \right)}^2}} + 5a\\
= \left| {2a} \right| + 5a\\
= 2a + 5a\\
= 7a\\
b)\sqrt {25{x^2}} + 3x\left( {DK:x \le 0} \right)\\
= \sqrt {{{\left( {5x} \right)}^2}} + 3x\\
= \left| {5x} \right| + 3x\\
= - 5x + 3x\\
= - 2x
\end{array}$
