Maths Olympiad Prep

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Algebra Difficulty 1.9 Junior Find the answer

What is the value of 16×16 \sqrt{16 \times \sqrt{16}} ?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

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

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