What is the ASCII (Alt+number) for the square root symbol (√) in Windows?

In short it's ALT + 251 (note, no preceding zero)

Unicode it is U-221A

http://www.fileformat.info/info/unicode/char/221a/index.htm

√

If that doesn't work then:

Press and hold down the Alt key.
Press the + (plus) key on the numeric keypad.
Type the hexidecimal unicode value (221A).
Release the Alt key.

Open regedit.exe

Navigate to HKEY_CURRENT_USER\Control Panel\Input Method and add a string or REG_SZ value EnableHexNumpad. Set the value to 1. Log out and log in.

Now you can use ALT <numpad +> 221A

As for why your ALT codes don't work:

Manufacturers of PCs have character sets in their hardware/firmware. These are called OEM code pages by Windows. Windows also has a standard Latin character set for english speaking regions called Windows-1252, which it uses for most non-unicode programs. When you type ALT 251 ¹ you use the OEM set which can vary between each PC (Mine is code page 850). When you type ALT 0251 û, it uses the Windows-1252 character set.

Some others were saying that ALT 8730 →or ALT 08730 <substitute (SUB) character> works but from my experience, any value above ALT 255 or ALT 0255 just gets converted back to a value between ALT 0 and ALT 255.

I used charmap and seeked to the position where the character U+221A is, clicked the buttons Select and Copy, then I pasted it where I wanted to use it.