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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_8 / The infinite product

Problem

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problem

The infinite product

\sqrt[3]{10} \cdot \sqrt[3]{\sqrt[3]{10}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{10}}} \cdots

evaluates to a real number

\sqrt{m}

. What is the value of m?

Plain-text mathematical notation (without MathML)

The infinite product
root[3](10)⋅root[3](root[3](10))⋅root[3](root[3](root[3](10)))⋯
evaluates to a real number √(m). What is the value of m?

Original LaTeX notation

The infinite product
\[\sqrt[3]{10} \cdot \sqrt[3]{\sqrt[3]{10}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{10}}} \cdots\]
evaluates to a real number $\sqrt{m}$. What is the value of m?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_8
task_id: 78a556ab-db18-5d20-ba62-2bd4a97a4e26
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f8
task_revision_id: 2
config / split: default / train

Official source

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