4797 yearsTo find how long it takes for seven-eighths (7/8) of a sample to decay:After 1 half-life, 1/2 remains (1/2 decayed)After 2 half-lives, 1/4 remains (3/4 decayed)After 3 half-lives, 1/8 remains (7/8 decayed)So we need 3 half-lives.Each half-life = 1599 years 3 half-lives = 1599 × 3 = 4797 years