The Four Fours puzzle using only $+$, $-$, $\times$, $\div$, $\sqrt{}$, and concatenation. Can we make $19$? I know the classic Four Fours puzzle, which asks to create whole numbers using exactly four "$4$"s combined via certain operations (arithmetic, concatenation, grouping, factorials, etc.), the exact roster of which can vary.  

I have tried this specific version of it:
You can use only the basic arithmetic operations ($\times \div + - $), square root ($\sqrt{}$), and concatenation (eg, "$44$" is allowed).


  How far you can go? I cannot go further than $18$. I am stuck with $19$ and does not seem that there is a solution for it.
Let $\#$ denote concatenation. That is, $4\#3 = 43$. Then 

$$(4 \# \sqrt 4) / \sqrt 4 - \sqrt4 = 42 / 2 - 2 = 19.$$

Not sure if you can use parentheses, but you would just have to perform concatenation first above all else.
According to Wikipedia, 19 has no solutions using only the operations you're describing.

Source: https://en.wikipedia.org/wiki/Four_fours#Solutions