With two dogs and a cat, that’s 12 paws roaming on my light gray tile floors with white grout. It’s bound to get dirty.
When it does, I make a simple solution to make the white grout look new again, without commercial cleaning products.
All you need:
2 parts baking soda
1 part bleach
A little goes a long way.
Apply a small amount of the paste on the grout and use a cleaning brush with a sturdy handle so that ii doesn’t break.