Given Data:
- Force A: 20√2N East of north
- Force B: 40N 60° N of W

Step 1: Resolve the Forces
To determine the magnitude of the resultant force, we need to resolve the given forces into their respective components.

Force A:
- The force is directed East of north, which means it has a component in the east direction and another component in the north direction.
- Let's assume the angle between the force and the north direction is θ.
- The component in the east direction can be calculated as A_east = A * sin(θ) = 20√2 * sin(90°) = 20√2 * 1 = 20√2N
- The component in the north direction can be calculated as A_north = A * cos(θ) = 20√2 * cos(90°) = 20√2 * 0 = 0N

Force B:
- The force is directed 60° N of W, which means it has a component in the north direction and another component in the west direction.
- Let's assume the angle between the force and the north direction is β.
- The component in the north direction can be calculated as B_north = B * cos(β) = 40 * cos(60°) = 40 * 0.5 = 20N
- The component in the west direction can be calculated as B_west = B * sin(β) = 40 * sin(60°) = 40 * √3/2 = 20√3N

Step 2: Calculate the Resultant Force
To determine the magnitude of the resultant force, we will add the respective components of the resolved forces.

- The component in the east direction = A_east = 20√2N
- The component in the north direction = A_north + B_north = 0N + 20N = 20N
- The component in the west direction = B_west = 20√3N

Now, we can calculate the resultant force using the Pythagorean theorem.

Resultant force (R) = √[(component in the east direction)^2 + (component in the north direction)^2 + (component in the west direction)^2]
R = √[(20√2)^2 + 20^2 + (20√3)^2]
R = √[800 + 400 + 1200]
R = √2400
R ≈ 48.99N

Therefore, the magnitude of the resultant force on the particle is approximately 48.99N.