How do I type special math symbols, such as square root and absolute value, using my Mac running Mojave version 10.14.6?

There are no math fonts installed by default into macOS, so you cannot just type these symbols without referring to third-party software (e.g. MathType which does install Math fonts), the equation editor where provided by the application, or rolling your own symbology via the macOS character viewer.

For instance, the current releases of Pages, Numbers, and Keynote — all have a built-in equation editor that uses a restricted LaTeX or MathML syntax, and will draw these math symbols/equations into the current document as inline text:

\sqrt{2} square root of 2

\lvert{x}\rvert absolute value of x

With each Apple or vendor software that supports it, there is the character viewer. When you press contol + command + Spacebar, in the current application, you will launch the Character viewer. In its upper left corner is a gear icon which offers Customize List… and you will want to select Math Symbols, Digits - All, and Technical Symbols to start. These will appear on the left panel of the Character viewer as categories.

The Character View has its own search field, and if you enter square r, that symbol will appear in the center panel of the character viewer. You double-click on that symbol to insert it into the current application text field from which you launched the character viewer. There is no searchable absolute value symbol, so you will want to search for vertical bar, double-click it to enter it, type the object of the absolute value, and then insert that vertical bar again.

Depending on your keyboard layout, opt-v will give √, and you can just us the pipe | symbol for absolute value. The pipe is on the backslash key on a US keyboard.

If you open the Keyboard System Prefs, Input Sources tab, you can view what characters can be typed using the modifier keys by holding down each modifier key combination.

You can also use the Emoji and Symbols (cntrl-cmd-space) panel to insert just about anything. If you expand the Character Viewer to full size, there is a section for Math symbols. You can also customize the list of categories from the gear menu on the expanded Character Viewer.