What can I use to dye my black roots a medium ash brown?

I naturally have black hair but I consistently dye my hair to a medium ash brown. Unfortunately, I'm low on cash and my black roots are showing? Do any of those at-home root touch up dyes work? If i buy one a shade or two lighter, will it work? I just don't want to have to bleach it first. Please help? =)

What can I use to dye my black roots a medium ash brown?
you don't need to bleach it first


your roots naturally pick up color faster so it will work


the only reason you would have to bleach it if your hair was dyed black


natural hair can be dyed any color


the only problem you might run into is getting your roots the same color as the rest of your hair