You should be able to to this directly with an update mysql.user set password=password('newpassword') where user = 'root' and host = 'localhost'.
But the root user is a little different, so you might want to check the MySQL docs for "gotcha"s. I'm pretty sure that there are explicit instructions on setting the root password, since that's one of the first things you're cautioned to do after installing MySQL server.
Alas, too often, I'm going the other direction, where I'm resetting the root password. For that you have to start the server in unsecured mode.
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