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Infinite square roots

Algebra Level 2

\[\large \sqrt{5 +\sqrt{5 + \sqrt{5 + \sqrt{5 + \cdots }}}} = \, ? \]

Give your answer to 3 decimal places.

1.442 2.791 3.142 1.753

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

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including olympiad champions, researchers, and professionals.

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View solutions

by Onkar Shirodkar

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