Calculate motor current consumption
Your calculation is correct. Your use of line-to-line voltage and division by the square root of 3 takes care of the per-phase aspect of the problem. You can probably find motors that size that have a bit higher efficiency and a bit better power factor, but that current is about typical for a 3-phase motor that size.

The slip is not needed, but it is a hint that this motor is not as efficient as you might expect. Typical slip for a 3-phase motor is about 2% to 3%. Slip is directly proportional to power lost in the rotor resistance. Another hint about efficiency and power factor is the number of  motor poles. 4-pole motors generally have the highest efficiency and power factor. Motors with more than 6 poles generally have a significantly lower power factor.