Đáp án:
\(j.\dfrac{{\sqrt 5 }}{2}\)
Giải thích các bước giải:
\(\begin{array}{l}
a.\sqrt {\dfrac{{12}}{{10}}.270} = \sqrt {12.27} \\
= 2\sqrt 3 .3\sqrt 3 = 18\\
b.\sqrt {55.77.35} = \sqrt 5 .\sqrt {11} .\sqrt 7 .\sqrt {11} .\sqrt 5 .\sqrt 7 \\
= 5.7.11 = 385\\
c.3 - 2\sqrt 6 + 2 = 5 - 2\sqrt 6 \\
d.{\left( {3\sqrt 2 } \right)^2} - 1\\
= 18 - 1 = 17\\
g.\sqrt 2 \left( {\sqrt 3 + \sqrt 2 } \right)\left( {\sqrt 3 - \sqrt 2 } \right)\\
= \sqrt 2 \left( {3 - 2} \right)\\
= \sqrt 2 \\
h.\left( {\dfrac{{2\sqrt 2 }}{{\sqrt 3 }} - 4\sqrt 6 + \dfrac{{5\sqrt 2 }}{{\sqrt 3 }}} \right)\sqrt 6 \\
= 2.2 - 4.6 + 5.2 = - 10\\
k.\dfrac{3}{2} - 2\sqrt {\dfrac{3}{2}} .\sqrt {\dfrac{2}{3}} + \dfrac{2}{3}\\
= \dfrac{{13}}{6} - 2 = \dfrac{1}{6}\\
g. - \left( {\sqrt 2 - 3} \right).\sqrt {9 + 2.3.\sqrt 2 + 2} \\
= - \left( {\sqrt 2 - 3} \right).\sqrt {{{\left( {3 - \sqrt 2 } \right)}^2}} \\
= \left( {3 - \sqrt 2 } \right).\left( {3 - \sqrt 2 } \right)\\
= 9 - 6\sqrt 2 + 2 = 11 - 6\sqrt 2 \\
f.\dfrac{{\sqrt 3 \left( {\sqrt 5 - \sqrt 2 } \right)}}{{\sqrt 7 \left( {\sqrt 5 - \sqrt 2 } \right)}} = \sqrt {\dfrac{3}{7}} \\
j.\dfrac{{\sqrt 5 \left( {\sqrt 2 + \sqrt 3 } \right)}}{{2\left( {\sqrt 2 + \sqrt 3 } \right)}} = \dfrac{{\sqrt 5 }}{2}
\end{array}\)
