How can I write a square root sign with the pop up keyboard on an iPad Pro?

The easiest way is to find that symbol browsing the Internet or copying it from here: √

When done, go to Settings>General>Keyboard>Text Replacement, tap the "+" add button and paste the math symbol in Phrase field, creating also the also the Shortcut (i.e. sqr). Tap done.

Everytime you write "sqr", you'll get "√"

Regards

Giulio

Presumably you refer to this - √

The iPad's native on-screen keyboard is quite limited in the characters that can be accessed. For access to a wider range of keys, you will need to install a suitable third-party keyboard App from the App Store.

Of those available, a popular choice amongst contributors here is Typefinity:

https://apps.apple.com/app/typefinity/id1512009869