Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\sqrt {48{{\left( {\sqrt {108} - 11} \right)}^2}} \\
= \sqrt {{4^2}.3.{{\left( {\sqrt {108} - 11} \right)}^2}} \\
= 4.\left| {\sqrt {108} - 11} \right|.\sqrt 3 \\
= 4.\left( {11 - \sqrt {108} } \right).\sqrt 3 \\
= 44\sqrt 3 - 4.\sqrt {108} .\sqrt 3 \\
= 44.\sqrt 3 - 4.\sqrt {{6^2}.3} .\sqrt 3 \\
= 44\sqrt 3 - 4.6.\sqrt 3 .\sqrt 3 \\
= 44\sqrt 3 - 72\\
b,\\
\sqrt {\left( {x - 1} \right)\left( {4{x^4} - 12{x^3} + 9{x^2}} \right)} \\
= \sqrt {\left( {x - 1} \right).{x^2}.\left( {4{x^2} - 12x + 9} \right)} \\
= \sqrt {\left( {x - 1} \right).{x^2}.{{\left( {2x - 3} \right)}^2}} \\
= \left| {x.\left( {2x - 3} \right)} \right|.\sqrt {x - 1} \\
c,\\
\sqrt {{{\left( {4 + \sqrt {18} } \right)}^2}} \\
= \left| {4 + \sqrt {18} } \right|\\
= 4 + \sqrt {18} \\
= 4 + \sqrt {{3^2}.2} \\
= 4 + 3\sqrt 2
\end{array}\)
