Is it bad that our washer and dryer are plugged into non-grounded outlets?

You should absolutely be concerned.

Here is some simple knowledge most people don’t know.

A power strip prevents your stuff from getting hurt. And it does a very bad job it it.

Grounding keeps you from getting killed/hurt. What having a ground does is that in the event that a wire comes lose inside the device and touches the case or anything metal it will push the power to ground instead of into you when you touch the metal case. This is super important since 99 of washers and driers have metal cases and deal with water.

edit :: my brother-in-law is a licensed electrician and we had a long talk about this one night about 10 years ago.

Yes. High voltage appliances like washers and dryers should be grounded.

”In the absence of a ground wire, if the appliance suffered some damage that caused a short circuit between the high voltage “hot” lead and the case of the appliance, the damage would make the case live and it would cause an electrical shock to anyone who touched it.
If the case is earthed by using a ground wire, if that same damage occurred the hot lead would immediately be shorted to ground and in theory cause the fuse or circuit breaker to open, thus eliminating the danger of a live case.”

You need GFCI receptacles and breakers for
outlets that are six feet from water.

Check your circuit box, too. If you have an electric dryer, it should be on separate breakers from everything else.

I would worry, the wiring maybe over fifty years old. The dryer plugged into a two prong outlet implies that it is gas dryer. The shock hazard is high. Is this a rental property? If it is I would have the landlord hire a licensed electrician to fix it.

Don’t let the landlord FIX- IT ! !

If you are living in the US and they are US appliances, then “Yes”, they should be grounded.
Do you have a voltmeter – and know how to use it? If yes then see if the appliance case has a voltage on it now. Measure from the center screw of the outlet to any metal on the appliance.

Oh wait . Is the adapter attached to the outlet with a third green wire attached to the center screw? If no then you should get it fixed.

It’s usually safe to use the adapters. If hot & neutral were reversed the breaker would have already blown. If you’re still worried about shock hazard, you could use a ground-fault interrupter. It will work even if the outlet is not grounded.

With old, ungrounded wiring, changing the receptacle to a 3-prong might still leave it ungrounded—it depends on the type of wiring, conduit, & boxes in use.

It is an NEC violation. Several above already answered this. You need to get someone to run a new cable (bx or romex) unless there is metal conduit feeding these outlets. Even with bx or conduit you still need a seperate ground wire. You can’t (by code) use the metal jacket on the bx cable or conduit itself as the ground (though technically they would still ground a short out).

Dryers usually run on 220 single phase (not 120 like a washer). The 220 outlet needs to be grounded as well. All the ground wire does is create an “amperage surge” if the hot touches any grounded metal surface to blow out the fuse or trip the breaker. A GFCI is very sensitive to any small amperage change and would protect you from being electrocuted. A GFCI is much more sensitive to current fluctuations than a typical fuse or breaker so they should always be used within 6ft of a water source.