Đáp án:
$\begin{array}{l}
a)\sqrt {19 - 8\sqrt 3 } + \sqrt {19 + 8\sqrt 3 } \\
= \sqrt {16 - 2.4.\sqrt 3 + 3} + \sqrt {16 + 2.4.\sqrt 3 + 3} \\
= \sqrt {{{\left( {4 - \sqrt 3 } \right)}^2}} + \sqrt {{{\left( {4 + \sqrt 3 } \right)}^2}} \\
= 4 - \sqrt 3 + 4 + \sqrt 3 \\
= 8\\
b)\sqrt {9{x^2}} - 3x\\
= 3.\left| x \right| - 3x\\
= - 3x - 3x\left( {do:x < 0} \right)\\
= - 6x\\
c)x - 4 + \sqrt {16 - 8x + {x^2}} \\
= x - 4 + \sqrt {{{\left( {x - 4} \right)}^2}} \\
= x - 4 + x - 4\\
= 2x - 8\\
d)\sqrt {6,{8^2} - 3,{2^2}} + \sqrt {21,{8^2} - 18,{2^2}} \\
= \sqrt {\left( {6,8 + 3,2} \right)\left( {6,8 - 3,2} \right)} + \sqrt {\left( {21,8 - 18,2} \right)\left( {21,8 + 18,2} \right)} \\
= \sqrt {10.3,6} + \sqrt {3,6.10} \\
= \sqrt {36} + \sqrt {36} \\
= 6 + 6\\
= 12
\end{array}$
