Why are the division rules for surds the way they are?

[gmax137]

The Wiki
https://en.wikipedia.org/wiki/Order_of_operations
provides some interesting info.
It states that

BODMAS meaning Brackets, Operations, Division/Multiplication, Addition/Subtraction. Sometimes the O is expanded as "Of" or "Order" (i.e. powers/exponents or roots).

 

[pbuk]

That's not the case with exponents. $2^{3^2} = 2^9 = 512$ and is evaluated as if written this way: $2^{(3^2)}$, but not as if written as $(2^3)^2 = 64$. With nested exponents, the evaluation goes from the top down -- i.e., right to left. See https://en.wikipedia.org/wiki/Exponentiation#Terminology.

But again this convention is not part of any UK syllabus: if there was any need for stacked exponentials the order would be made explicit ($2^{(3^2)} = 262144$ or $(2^3)^2 = 64$).

BTW I'm not sure that BODMAS is a thing. The E and I parts of the acronyms represent 'exponent' and 'index' respectively. If there's a word that corresponds to O I'm not aware of it.

Order. BODMAS was the standard term used in the UK until [a few years ago] when it was replaced with BIDMAS in the national curriculum, although you will still see a lot of materials using BODMAS. We have never used E for exponentiation (or P for parentheses) here.

 

[pbuk]

BODMAS meaning Brackets, Operations, Division/Multiplication, Addition/Subtraction.

That is wrong - note that none of the references say this. I will correct some time.

 

[gmax137]

Well, I was just pointing to Wiki. I do agree with you, "operations" doesn't make much sense.

As always, Wiki is... wiki.

 

[Mark44]

But again this convention is not part of any UK syllabus: if there was any need for stacked exponentials the order would be made explicit ($2^{(3^2)}$ or $(2^3)^2 = 64$).But

That's all well and good about the UK syllabus, but stacked exponentials without parentheses do occur in the wild; e.g., $e^{x^2}$ and similar. Some readers would recognize that x should be squared before the exponentiation, but not all would. If the mathematics community would take a leaf from computer science about precedence and associativity, it's my view that this would be a good thing, possibly eliminating most of the stupid, click-bait Youtube videos like the one in the OP of this thread.

 

[paulb203]

I have lived on this planet the better part of six decades, most of it surrounded by science and math, and this is the first time I have ever heard the term "surd". I assumed it was maybe an unfamiliar acronym for a term I am familiar with, but no, it's a straight-up word, from Latin, that has simply eluded me all this time.

My life is a lie.

When you assumed it might be an acronym did you consider, Simplify Ur Roots, Dude?