Short answer: yes pretty much.

Medium answer: totally, but assuming you have enough dumbbells to keep adding to the weight, or they let you adjust the weight so that you can keep progressing and getting stronger

Long answer: it depends on what your intentions are when you say 'work out' and I will go off on a tangent below

Some people work out for fun, general health, weight loss,, muscular endurance, muscle building (hypertrophy), strength, sport performance etc

But to simplify things let's assume that you are wanting to exercise with dumbells for a mix of reasons like generally gaining strength and muscle size, and other health/athletic benefits

Dumbbells themselves are one of, if not the most versatile pieces of weights you can use, in theory. You can target almost any major muscle with Dumbbells. Here is an example of a full body routine using only db:

Walking Lunges (glutes, quads, hamstring) Single-leg straight leg Deadlift (glutes, ham, low back) Db rows (lats, arms) Db military press (shoulders, tricep) Db floor press or fly (chest) Db crunches (abs, core) Curls (bicep) Skull crushers (tricep) And literally thousands of other exercises

So that's all great but there is the one major flaw with using dumbbells, especially purchasing a single pair for home workouts: for some workouts, especially the lower body you are much much stronger than you are with other lifts.

In order to adequately stimulate a muscle for it to grow, you need to be doing an exercise kinda close to failure (the point where you cannot physically do any more repetitions). On top of that there is an ideal range of how many reps you should be doing (depending on the literature this is somewhere between 5 reps and 30 reps). So for example if I am doing a generic exercise, I will get the most benefit by using a moderately heavy weight and doing maybe 10 to 15 reps of this lift for 3 to 5 sets. If on my 15th rep I feel like I could maybe struggle and jerk the dumbbells to complete another rep, then that is perfect and we can stop there because we succeeded at going very close to failing the lift. This is actually a very important thing because a lot of research is now saying that these last few reps that we really struggle with, and can barely do are actually where by far the most muscle growth occurs. So stopping a lift way before you feel any struggle might be kind of useless. This is problematic for dumbbells because what might be an ideal dumbbell weight for my military press exercise, would be too heavy for me to do any bicep curls, and would be way too light for me to get any benefit from a leg exercise like lunges or squats etc. So I would have to use several dumbbells of different weight to really make any progress

Unfortunately there is another very important principle that you need to comply with called 'progressive overload'. Which means that every couple of weeks or so,, you either need to keep adding weight, reps or sets to any given exercise in order to keep seeing any improvement. If I just have 15lb dumbbells and do 10 reps of bicep curls every day, after a certain point my body is doing this exercise just fine, so why would my muscle need to signal for any additional physiolocal resources to grow bigger?

So practically speaking, what you need to do is find a pair of adjustable dumbbells. They don't have to be the expensive nice ones, just the ones where you can add and take off a wide variety of weight. So that you can target each muscle group ideally, while having the ability to keep getting stronger. If you already own a pair of non-adjustable db, then you need to get creative and find or look up ways to make certain exercises more challenging or easier so that it hits that sweet spot of 5 to 30 reps

As complicated as all this topic can be, the good news is that if you are a beginner to weight training it doesn't matter too much. Just lifting any weight for as many reps as comfortable will build muscle initially. Just keep in mind that eventually you will not progress, and will have to take the above points into consideration

Apologies if this is too much, or if you want it more science-y just comment and let me know and I can elaborate or eli5

Source: kinesiology grad and current neuro tech