A multimeter will tell you in seconds.

Yes. Grab a multimeter and set it to continuity (the beep mode or lowest resistance). You need to access both ends of the cord – the prongs on the plug and the slots in the socket.

Test each conductor separately. Stick one probe on a prong and the other on the corresponding slot on the same wire (e.g., the wide prong to the wide slot). If it beeps, that wire is continuous. If it doesn’t, you’ve found the broken conductor. Repeat for the other prong/slot pair. No cutting required.

Just don’t plug the cord into a wall while you’re testing – you’re only using the multimeter’s battery for continuity. If you don’t have a multimeter, a cheap continuity tester from the hardware store does the same thing for under ten bucks.

This test takes two minutes and saves you from tossing a perfectly fine cord.