What change should be expected in the velocity of a body to maintain the same kinetic energy, if its mass is increased sixteen times? How?

Hello!
Kinetic energy is that part of full energy which a body has due to its motion. The formula for kinetic energy is E_k = (m V^2)/2, where m is the mass and V is the speed (regardless of direction).
Usually a body remains the same during its motion, and the mass of the body also remains the same. In our problem, the mass of the body is supposed to increase 16 times, roughly speaking some other bodies will join our initial body.
In such a case, its kinetic energy becomes E'_k = ((16 m) V^2)/2 = 16 E_k. To compensate this change by a speed change, we have to reduce V^2  16 times, which means to reduce V  sqrt(16)=4 times.
This is the answer: body's speed must be reduced 4 times to maintain the same kinetic energy.