Use the Force

A constant force accelerates an object from rest across the (x,y) plane. The work done in the x direction is 3 J. The work done in the y direction is 4 J. If the component of the force in the x direction is 1 N, then the force has a magnitude which can be expressed as \[\sqrt { \frac { a }{ b } } \] where a and b are coprime integers. What is the value of \[a+b\]

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