2 Answers

Assuming that the mass of the object cannot change then to triple the momentum requires the velocity to increase by a factor of three.
Kinetic energy is proportional to the square of the velocity ( 1/2 m v^2 )
so it must increase by 3^2 or a factor of 9 times.

P = m*v = momentum
E = ½m*v² = kinetic energy
Ergo,
E = ½m*[P/m]²
E = ½[P²/m], or, E is proportional to momentum squared