Yes, into the / directory.
If there is a public_html directory is totally up to the hosting service. Some have it, others don't. And if they have it, sometimes the name is different, like www, inetpub, htdocs etc.
If there is a public_html directory is totally up to the hosting service. Some have it, others don't. And if they have it, sometimes the name is different, like www, inetpub, htdocs etc.