Explanation:

- The area of the floor of the cubical room is given as 147 m².

- A cube has equal side lengths, so if the floor area is 147 m², then each side of the floor (and the room) is $\sqrt{147}$ m.

- Calculating $\sqrt{147}$, we find it's approximately 12.12 m.

- The longest rod that can fit inside the cube is the space diagonal, calculated by the formula: $a\sqrt{3}$, where $a$ is the side of the cube.

- Plugging in the value, 12.12 * $\sqrt{3}$ ˜ 20.98 m.

- Option:3, 21 m is correct as 20.98 m rounds to 21 m.