There is a big cube and some small cubes on a table. The volume of the big cube is 125 cubic in. If the difference between the volume of the big and small cubes is 98 cubic in, then the difference between their side lengths is ______ in.

The correct option is D $2$
$\text{Detailed step-by-step solution:}$
Volume of the the big cube $=125$ cubic in
Difference between the volume of the big and small cubes $=98$ cubic in
So, the volume of a small cube $=125-98=27$ cubic in
Formula to find the volume of a cube $=a^3$(if a is the length of each side of the cube)

Considering the big cube, $a^3=125$
$\Rightarrow \sqrt[3]{3a^3}=\sqrt[3]{3125}$ (taking cube root on both the sides)
$\Rightarrow a=\sqrt[3]{35\times 5\times 5}$ (finding the factors of 125)
$\Rightarrow a=5$ (solve for $a$)

Considering the small cube, $a^3=27$
$\Rightarrow \sqrt[3]{3a^3}=\sqrt[3]{327}$ (taking cube root on both the sides)
$\Rightarrow a=\sqrt[3]{33\times 3\times 3}$ (finding the factors of $27$)
$\Rightarrow a=3$ (solve for $a$)
So, the difference between the side lengths $=5-3=2$ in.

So, option A is the correct answer.