Is there any other way to write great-great-great-great-great-great-granddaughter?
Yeah, descendant.
Only specify the number of generations and gender if it is required.
Also, depends on the writing style and rhetorical mode.
@Pat works for fiction books?
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Depends on the style. If it's dialogue, it depends on the character, too. Those 'greats' may be useful in context.
