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Problem 354

Algebra Difficulty 2.0 Prove it UKMT Senior Kangaroo · United Kingdom · 2021

The geometric mean of a set of $n$ positive numbers is defined as the $n$ -th root of the product of those numbers. Yasmeen writes down a set of four numbers which have a geometric mean of $2048$ . Zak writes down a set of four numbers which have a geometric mean of $8$ . What is the geometric mean of the combined set of the eight numbers written by Yasmeen and Zak?

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