Laravel 'Access denied for root' due to running my app in a virtual box?

I am working through the Laracasts db tutorial to learn how to work with databases in a properly 'Laravel' way. I have set up a local MySql instance and I have run the migrations to set up my tables and fields and also for the built in Laravel user authentication/login/register functions. It all works perfectly on the command line. My user 'root' and password allow me to browse my new db, select and add records as you might expect. However, when I run the app through my browser I get 'Access denied for user root'.

Is this because I'm running my app under 'Homestead/Vagrant'? Do I need to copy my MySQL database to the vagrant box somehow - maybe setting it up with the homestead yaml file? I'm confused!

via Chebli Mohamed