How many whole numbers are between √8 and √80?

1986 AMC 8 Problem 7 — Solution

1986 AMC 8 Problem 7

Attempt Problem 7 of the 1986 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1986 AMC 8 solutions, or check the answer key.

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How many whole numbers are between $\sqrt{8}$ and $\sqrt{80}?$

$5$

$6$

$7$

$8$

$9$

Answer: B

Concepts:counting integers in a range perfect square

Difficulty rating: 820

Solution:

Since $\sqrt{8} \lt \sqrt{9} = 3$ and $\sqrt{80} \lt \sqrt{81} = 9,$ the whole numbers strictly between $\sqrt{8}$ and $\sqrt{80}$ are $3,$ $4,$ $5,$ $6,$ $7,$ $8.$ There are six of them.

Thus, the correct answer is B .

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