Plug in a lamp and wiggle the cord.
Yes, you can test an extension cord for internal breaks without a multimeter — just plug in a simple lamp or small appliance (something that draws a little power) and flex the cord along its length.
Plug the lamp into the extension cord, turn it on, and then slowly bend the cord at different points — especially near the ends and where it’s been kinked or pinched. If the lamp flickers or goes out when you bend a certain spot, you’ve found the internal break. No flicker means the cord is probably fine.
This won’t tell you about a partial break that only shows under a heavy load, but for most household extension cords — the kind used for lights, fans, or tools — the wiggle test catches the common failures. If the lamp goes out entirely, the cord is dead. Check the plugs first for bent prongs or loose connections; those are fast fixes.
If it flickers, replace the cord. A broken internal wire can overheat or arc. Not worth the risk.