Maths Olympiad Prep

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, 2020

Algebra Difficulty 1.2 Junior Find the answer Canada

The value of ( ⁣ ⁣81+812\sqrt{\dfrac{\phantom{\big(}\!\!\sqrt{81}+\sqrt{81}}{2}} is

33
1818
2727
8181
162162

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

Solution

Calculating, ( ⁣ ⁣81+812=9+92=9=3\sqrt{\dfrac{\phantom{\big(}\!\!\sqrt{81}+\sqrt{81}}{2}} = \sqrt{\dfrac{9+9}{2}} = \sqrt{9} = 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.