The Google Webmaster Tools Remove URL section allows you to specify a page URL to be removed from the index, or cache, or both.

However, I want to remove just the home page, which is /

I want to remove it from the cache because it is indexed when the "under construction" page was up.

This URL is not recognised by the Remove URL section as an individual page. Instead Google assumes you want to remove the entire website from the index.

I've specified /index.php and /index.html to be removed from the cache, but this is not the URL listed in the search results for the home page I want removed from the cache.