Đáp án:
$\begin{array}{l}
a)\sqrt 5 .\sqrt {45} \\
= \sqrt 5 .\sqrt {9.5} \\
= \sqrt 5 .3\sqrt 5 \\
= 3.5\\
= 15\\
b)\sqrt {12} - \sqrt {27} + \sqrt 3 \\
= 2\sqrt 3 - 3\sqrt 3 + \sqrt 3 \\
= 0\\
c)\sqrt {6 + 2\sqrt 5 } + \sqrt {6 - 2\sqrt 5 } \\
= \sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} + \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} \\
= \sqrt 5 + 1 + \sqrt 5 - 1\\
= 2\sqrt 5 \\
d)\dfrac{1}{2}\sqrt {32} + \sqrt {98} - \dfrac{1}{6}\sqrt {18} \\
= \dfrac{1}{2}.4\sqrt 2 + 7\sqrt 2 - \dfrac{1}{6}.3\sqrt 2 \\
= 2\sqrt 2 + 7\sqrt 2 - \dfrac{1}{2}\sqrt 2 \\
= \dfrac{{17}}{2}\sqrt 2 \\
e)2 + \sqrt {{{\left( {2 - \sqrt 7 } \right)}^2}} \\
= 2 + \sqrt 7 - 2\\
= \sqrt 7 \\
f)5\sqrt 8 - \dfrac{7}{2}\sqrt {72} + 6\sqrt {\dfrac{1}{2}} \\
= 5.2\sqrt 2 - \dfrac{7}{2}.6\sqrt 2 + 6.\dfrac{{\sqrt 2 }}{2}\\
= 10\sqrt 2 - 21\sqrt 2 + 3\sqrt 2 \\
= - 6\sqrt 2 \\
g)\sqrt {12} - \sqrt {75} - \sqrt {27} \\
= 2\sqrt 3 - 5\sqrt 3 - 3\sqrt 3 \\
= - 6\sqrt 3 \\
h)\sqrt {3 + 2\sqrt 2 } - \sqrt {6 - 4\sqrt 2 } \\
= \sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}} - \sqrt {{{\left( {2 - \sqrt 2 } \right)}^2}} \\
= \sqrt 2 + 1 - \left( {2 - \sqrt 2 } \right)\\
= \sqrt 2 + 1 - 2 + \sqrt 2 \\
= 2\sqrt 2 - 1\\
k)2\sqrt[3]{8} - \sqrt[3]{{27}} + \sqrt[3]{{64}} + 3\sqrt[3]{{ - 125}}\\
= 2.2 - 3 + 4 + 3.\left( { - 5} \right)\\
= 4 - 3 + 4 - 15\\
= - 10
\end{array}$
