Problem 2 · 2021 Math Kangaroo
Medium
Algebra & Patterns
estimate-and-pick
How many integers are in the interval \(\left(20-\sqrt{21};\ 20+\sqrt{21}\right)\)?
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Answer: A — 9
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Hint 1 of 2
Estimate √21 to one decimal place.
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Hint 2 of 2
The interval is open, so count the whole numbers strictly between the two endpoints.
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Approach: bound the endpoints and count integers
- √21 is between 4 and 5 (about 4.58), so the interval is roughly (15.42, 24.58).
- The integers strictly inside run from 16 to 24.
- That is 24 − 16 + 1 = 9 integers.
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