Q:

How to Teach Middle School Students to Read Square Roots?

This exact quote from my standard American Algebra 1 textbook states when  first introducing rational square roots:

$\sqrt{49} = 7$  is read "The positive square root of $49$ equals $7$."
$-\sqrt{49} = -7$ is read "The negative square root of $49$ equals $-7$."

In the next lesson, the expression $5\sqrt{3}$ is used in an example of simplification, but no instructions are given on how to "read" it?
I think these are some possible ways:

$5\sqrt{3}$ is read "5 the positive square root of 3."
"5 square root 3."
"5 root 3."

Following the textbook's instructions from the previous lesson, the first way seems most appropriate; but the third way has the least words? Is  there a "correct" way to read $5\sqrt3$ and are there any other possibilities?

A:

I would say that the word of is pretty important here, and as long as you get that correct, the rest is less important.
Using the word of consistently when a function is being applied to an input, and talking about the fact that you are doing this, will help ward off a lot of the following kinds of mistakes that I see in my (much later) classes:

Question: Solve for $x$. $\sin x = z$.
Student solution: $x = \frac{1}{\sin}z = \csc z$  

The mistake here is that it is unclear to the student that there are different kinds of mathematical objects: some are numbers, but some are functions/operations. 

So my answer is that saying "3 root 5" for $3\sqrt5$ is a dangerous abbreviation, because it begins to confuse this issue earlier than it needs to be confusing (What kind of object is "root" anyway?).
As a result I would prefer at least "3 square root of 5." 

Similarly "sine of x" for $\sin x$ and "ell en of x" for $\ln x$.

A:

I'm not aware of any "official" version, the text that you quoted not withstanding, so any response is going to be mostly just personal preference.
With that said, I wouldn't read either expression the way your textbook wrote them.  "the positive square root" is redundant.  The square root of a number, in this context, is always positive so I would just read the first version as "the square root of 49".  
For your second expression, I wouldn't refer to "the negative square root" for the same reason, i.e. there's no such thing.  This phrasing implies that there's a positive version of the square root and a negative version which isn't the case.  I would read it as "minus the square root".
With respect to your last example, I agree that (1) seems to be the most consistent with what you posted from the textbook.  However, it's also excessively wordy and the lack of a verb after the five makes it sound awkward.  I would read it as, "three times the square root of five".

