Hi Amy,
There are a number of reasons that your Nest could be beeping, including low batteries, a sensor failure, or if a Protect has reached its expiration date. These beeps should be accompanied by a yellow pulsing of the light ring on the Protect.
If you are confident that it is the batteries, then these will need to be replaced with Energizer Ultimate Lithium AA (L91) batteries.
If you are not sure what the issue is, then press the button on the Protect and it should tell you what issue has been identified. You can also consult this page
here which can help to identify the exact cause of the issue.
Let me know how you get on.
-From Phil S UK, Silver Product Expert.