Answer
The days will get longer. The angular speed of the Earth decreases.
Work Step by Step
The Earth may be considered as the system. There is no net external torque. The angular momentum of the system is conserved.
The mass of the polar ice caps is originally quite close to the axis of rotation. After the ice caps melt, the water spreads out over the Earth’s surface, moving mass away from the axis of rotation, increasing the moment of inertia of the Earth. Recall that angular momentum is conserved.
$$I_{old}\omega_{old}= I_{new}\omega_{new}$$
The moment of inertia increases, so the angular velocity decreases, and the length of the day becomes longer.
