Before the advent of calculators they had useful ready made tables for the main functions:sines,cosines logs etc..., do you know if tables of square roots were ever produced or in use?
I never heard of it, yet, it would be very easy to produce, since it is enough to find the roots of numbers from 1 to 100.
Pretty much every mathematics textbook (school or college) before the early 1980s (and many even up to the late 1980s), at the algebra level or above, as well as many (most?) chemistry and physics and engineering textbooks, had such a table at the back of the book (as an appendix or something, where "selected answers" and "index" and "glossary" would appear). Often the entries would be for both $\sqrt{n}$ and $\sqrt{10n},$ which was enough to allow you to easily get approximations for any magnitude-size numbers. For example, to find an approximation for $\sqrt{3880},$ use $n=3.88$ and look in the $\sqrt{10n}$ entries, since
$$ \sqrt{3880} \; =\; \sqrt{1000\times 3.88} \; = \; 10\sqrt{10 \times 3.88}. $$
There were stand-alone (i.e. as separate books) tables also, such as the following, where square roots from $1.00$ to $9.99$ by increments of $0.01$ are on pp. 16-17 and square roots from $10.0$ to $99.9$ by increments of $0.1$ are on pp. 18-19:
Mathematical Tables for Class-Room Use by Mansfield Merriman (1915) https://archive.org/details/mathematicaltabl00merrrich
When I was in high school I owned (purchased in 1974) and used the 20th edition (1973) of the CRC Standard Mathematical Tables. On pp. 71-90 you'll find a table having column entries for $n^2$ and $\sqrt{n}$ and $\sqrt{10n}$ and $n^{3}$ and $\sqrt[3]{n}$ and $\sqrt[3]{10n}$ and $\sqrt[3]{100n}$ from $n=1$ to $n=1000$ by increments of $1.$ In high school I also owned (I no longer seem to have it, however) Logarithmic and Trigonometric Tables to Five Places by Kaj L. Nelson (in the well known Barnes and Noble College Outline Series of books), and other people I knew (in college) had the Schaum's Outline Series of Mathematical Handbook of Formulas and Tables by Murray R. Spiegel (1968), which I didn't have a copy of back then but a few years ago I saw and purchased a copy of a later printing (the 1990 printing) at a local used bookstore (square roots are on pp. 238-239). However, in looking at the Schaum's book now, it's more of a handbook of formulas (algebraic, trigonometric, calculus, series, special functions, etc.) than a table of numerical values for computational use.
For other such books, try this search and similar searches. For tables at the back of textbooks, simple archive.org and google-books searches will give you hundreds (if not thousands) of examples where you'll find square root tables at the back of the book.
The Babylonian clay tablet from around 1700 BC known as YBC7289, since it's one of many in the Yale Babylonian Collection has a diagram of a square with one side marked as having length 1/2. They took this length, multiplied it by the square root of 2, and got the length of the diagonal.
Given that square roots were in use then, it would have made sense to create a table of such, rather than repeating the labour in calculating the result.
In addition to the existence of such tables, (in the later 1960's, for example) high school math classes included some lessons on (linear) interpolation from the values given in tables.
And some of us wondered about higher-order interpolation, and so on, which does nicely lead to many topics in calculus ... and splines and other stuff.
Slide rules were a very good competitor to "tables", in many situations, since they could give quicker answers (tho' somewhat lower precision) and were more portable.
