Maths Olympiad Prep

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, 2015

Algebra Difficulty 1.4 Junior Find the answer Canada

The value of 16×16\sqrt{16 \times \sqrt{16}} is

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Solution

Evaluating, 16×16=16×4=64=8\sqrt{16\times \sqrt{16}} = \sqrt{16 \times 4} = \sqrt{64} = 8 Since 8=2×2×2=238 = 2\times 2\times 2 = 2^3, then 16×16=23\sqrt{16\times \sqrt{16}} = 2^3.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.