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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7.

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

Small hint:

Find perfect squares just above

8

and just below

80

Big hint:

\sqrt{8}

is between

2

and

3,

and

\sqrt{80}

is between

8

and

9

Solution:

Since

2 \lt \sqrt{8} \lt 3

and

8 \lt \sqrt{80} \lt 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 .