Here we can use the formula:- \(\sqrt{(y2 -y1)^2 + (x2 -x1)^2}\)

Here y2= \(5\sqrt{3}\); y1 = \(2\sqrt{3}\)

x2 = \(3\sqrt{2}\) and x1 = \(\sqrt{2}\)

So putting the values in the formula we have:

= \(\sqrt{(5\sqrt{3}-2\sqrt{3})^2+(3\sqrt{2}+\sqrt{2})^2}\)=\(\sqrt{(3\sqrt{3})^2+(4\sqrt{2})^2}\) = \(\sqrt{59}\)

Now we know \(7^2\)=49 and \(8^2\)=64, so 59 should in between \(7<\sqrt{59}<8\).

Therefore only D. gives a possible value