Problem 2 · 2009 Math Kangaroo
Easy
Algebra & Patterns
estimate-and-pick
Which of the following numbers is biggest?
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Answer: A — \(\sqrt{2}-\sqrt{1}\)
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Hint 1 of 2
Each choice is √(n+1) − √n; think about how that gap behaves as n grows.
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Hint 2 of 2
Consecutive square roots get closer together, so the gap is largest at the start.
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Approach: the gap between consecutive square roots shrinks
- Every option is √(n+1) − √n, which equals 1/(√(n+1)+√n).
- A bigger denominator means a smaller value, and the denominator grows with n.
- So the smallest n gives the biggest value: √2 − √1.
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