I've just come across this convoluted mess. RoI has its own equivalents to our 08 disaster, and for much the same historic reasons. 1800 is their 0800, 1850 is their 0845, and 1890 is their 0870. All are followed by six-digit numbers, and CANNOT be dialled from outside RoI.
So, the number, say, 1850 940940, cannot simply be prefixed by +353. You'd instead be dialling +353 1 850 9409 (the trailing 40 will be ignored), and you'll upset some poor Dubliner with this phone number. You would need to get their geo number, which is +353 1 450 2113 (or 01 450 2113 from within RoI).
Irish numbers either start with 01, 021-098 (with 086 and 087 being mobiles), or 1800/1850/1890.
Depending on your phone provider and what they charge, it may well be cheaper to dial the international Irish number than the 0870 number. I don't know as I pay BT for a call to RoI as if it were a UK national geo call (5.5pph or whatever it is now).
Incidentally, they moved their directory enquiries services to 118 numbers years before we did. Shame we didn't learn from the disaster that created. But that's another story...