I beg to differ. And there's the crux (side pun intended) of your problem.

What does a Jew in the first century need to do in order to enter the temple and make the sacrifices of a Nazarite Vow?

Learn that and you'll have your answer.

The purification is actually MORE than just tevilah (baptism), but it definitely includes at least one tevilah and probably several. It's well-know Jewish history for those who care enough about the Jewish roots of the faith to learn that Jewish history of the New Testament. For those that choose not to educate themselves on that history, they go on and on about the meaning of Greek words in all kinds of wrong directions on a great many New Testament concepts.

As far as baptism is concerned ... its only the top of your head that really matters.

Go to minute 21:35 in this link ... it will be cleared up forevermore.

Why have two distinct words for baptism and purification? The root word for baptism appears many times in the LXX. Not a single one refers to purification by washing in water. It seems clear that this is a different concept than the purification rites. Else why the two words?

If ritual bathing or washing was referred to throughout the LXX as baptism, then we'd have something to see. But it wasn't. Not once, not a single time. Edit to clarify - the ritual rites you are saying as baptism. The word baptize is used in Kings with a seven time washing to cure a skin disease. I can't remember the exact passage. But either way it's not the temple rites you're talking about.

The use of the LXX as a means to understand the NT is not only reasonable but necessary. The LXX was used and referred to by the authors of the NT. It is a key to referencing the words, to see how they are used in the It and the new. If the NT was written originally in Hebrew, it would make sense to do the same examination of the Hebrew OT to see exact word for word comparisons. But it wasn't.

So again. I don't agree. For you to be right, the whole world has to be wrong.

Let me put it another way. You're saying this ritual washing is the same thing as a baptism - or perhaps more accurately that baptism is just an extension of existing ritual washing practices.

For this to be true we'd expect to see the words used interchangeably, one or the other. But you don't. Ritual washing with water and baptism are distinct ideas and they're never mixed and matched in anybody's if the discourses. The baptism of Christ is referred to as a single event, a seminal event, a saving event. Not a repeated event, and certainly not a business-as-usual washing that everyone was always already doing. It doesn't make sense.

The Greek word "sun-ago-ga" (synagogue) is also found nowhere in the Old Testament. By your logic you would conclude they did not exist in the first or second century BC. But they were everywhere then, and in the time of Yeshua; as were Mikvehs. They've found 200 of these in Jerusalem alone from this time period and 50 of those are in the immediate vicinity of the Temple. It was likely that it was impossible to approach the temple on any of the created pathways without passing through one or more of these "baptismals". Right, wrong, or indifferent, Paul was baptized in these when he approached the temple. Assign it whatever meaning you want. Baptisms were done many places and for many reasons in first century Jewish culture (not just the baptism of John and the baptism of Yeshua) and they are not only not counted as wrong, but they participated in them (such as Paul did in the Temple).

There are a great many things common in first century Jewish culture such as tevilah, covenants, betrothals, etc that are alluded to; but not completely explained in scripture, because they were so common for people of the day there was no need to explain them. They all knew it. Because the lived it. It's basically like Corporal Barnes knowing where the mess hall was even though it was never written in the Marine Outline for Recruit Training nor the Standard Operating Procedures, Rifle Security Company, Guantanamo Bay, Cuba. Those are the facts. And they are undisputed. Just study them.

Sorry, I'm not disputing that at all. What I am disputing is your conclusion that follows that - namely, that the baptism commanded by Christ and taught by the Apostles in the NT is identical to these ritual washings, whether we call them immersions in a general sense (ie, baptize, to dip or immerse) or baptism in a specific one (to baptize in the name of the Trinity).

In other words, I don't think the Apostles would have identified that the baptism they performed with people was the same as the ritual washing we see in the Law. Never mind that the Pharisees were annoyed on more than one occasion about Christ and His apostles not doing some of these ritual washings.

Baptism is different. I'm disputing that what St Paul did in this verse is baptism in the specific sense of "be baptized in the name of Jesus".