**Root Force Calculator**

Enter the values of force component along the x-axis, F_{x(N)} and force component along the y-axis, F_{y(N)} to determine the value of root force, RF_{(N)}.

**Root Force Formula**

The root force is calculated to find the resultant force magnitude when multiple forces are acting along different axes (for example, along the x and y axes). It is derived using the Pythagorean theorem in the context of vector addition.

Root force, RF_{(N)} in Newtons is calculated by the squareroot of the sum of square of force component along the x-axis, F_{x(N)} in Newtons and square of force component along the y-axis, F_{y(N)} in Newtons.

Root force, RF_{(N)} = √( F_{x}^{2}_{(N)} + F_{y}^{2}_{(N)} )

RF_{(N)} = root force in Newtons, N.

F_{x(N)} = force component along the x-axis in Newtons, N.

F_{y(N)} = force component along the y-axis in Newtons, N.

__Root Force Calculation:__

- Given a situation where two perpendicular forces are acting on an object with magnitudes of 3 N and 4 N along the x and y axes, respectively. Calculate the root force.

Given: F_{x(N)} = 3N, F_{y(N)} = 4N.

Root force, RF_{(N)} = √( F_{x}^{2}_{(N)} + F_{y}^{2}_{(N)} )

RF_{(N)} = √( 3^{2} + 4^{2} )

RF_{(N)} = √( 9 + 16 )

RF_{(N)} = √( 25)

RF_{(N)} = 5N.

- A root force (RF) of 10 N and a force along the x-axis of 6 N, calculate the force along the y-axis.

Given: F_{x(N)} = 6N, RF_{(N)} = 10N.

Root force, RF_{(N)} = √( F_{x}^{2}_{(N)} + F_{y}^{2}_{(N)} )

F_{y(N)} = √( F_{x}^{2}_{(N)} + F_{y}^{2}_{(N)} )

F_{y(N)} = √( RF^{2}_{(N)} – F_{x}^{2}_{(N)} )

F_{y(N)} = √( 10^{2} – 6^{2})

F_{y(N)} = √( 100 – 36 )

F_{y(N)} = 8N.