First of all, you should know that 'strawberry begonia' is not a begonia (or a strawberry!) Its botanical name is Saxifraga tomentosa. It is hardy here in south Louisiana, and I think in quite a bit colder zones, but I don't know how cold. Makes an excellent groundcover or rock garden plant. But I assume you mean to grow it as a houseplant? Not too sure about that, but since it does well here where it's warm and humid (or HOT and humid lately) I would guess you'd need to be sure the air isn't too dry where you're growing it. Good light. Shouldn't be too hard to grow I think--I planted it and let it do its thing. (I should add, It's 'thing' was to die when I lived overseas for a year.)

Up here in Ontario Canada, they are sold more commonly as indoor plants only.

In my book The Complete Book of Houseplants by B. Mitchell it advises: water so soil is always moist but not soggy. Good drainage is essential. Add a weak fertilizer once every 4 to 6 weeks during the growing season. Increase humidity in temperatures above 65 F (18 C) by mist spraying or standing pot on tray of dampened pepples. "Never allow the plants to remain in hot, full sun for any length of time, but do not put in dense shade either. A little direct sunlight -- say an hour or two of early morning sun every day, or a little longer for the variegated S.s. "Tricolor"..."

Haven't grown one in a long time so can't speak from experience at this time. Sounds to me like care for an African Violet, although I'm no expert on that either but do have a couple that successfully bloom for me regularly.

They are hardy in middle TN where my parents live if that helps you any. I grow mine outdoors in a semi-shady area where they slowly spread out making a nice ground cover in the Atlanta area. They even are hardy in a container in our area as well.