$\text{I.}$

$\sqrt{18}=\sqrt{9}\cdot \sqrt{2}=3\cdot \sqrt{2}$

$\text{I. B}$

 

$\text{II.}$

$\sqrt{40}=\sqrt{5}\cdot \sqrt{8}$

$\text{II. A}$

 

$\text{III.}$

$5\cdot \sqrt{10}=\sqrt{25}\cdot \sqrt{10}=\sqrt{25\cdot 10}$

$\text{III. C}$

 

$\text{IV.}$

$\frac{\sqrt{1}}{6}\cdot \sqrt{96}\cdot \sqrt{5}=\sqrt{\frac{1}{6}\cdot 96\cdot 5}=\sqrt{16\cdot 5}=\sqrt{16}\cdot \sqrt{5}=4\cdot \sqrt{5}$

$\text{IV. A}$