1988 AMC 8 Problem 11

Attempt Problem 11 of the 1988 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 1988 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

11.

The value of 164\sqrt{164} is
4242
less than 1010
between 1010 and 1111
between 1111 and 1212
between 1212 and 1313
Answer: E
Concepts:perfect squareestimation
Small hint:
Find perfect squares just below and just above 164164
Big hint:
122=14412^2 = 144 and 132=16913^2 = 169
Solution:
Since 122=14412^2 = 144 and 132=169,13^2 = 169, and 144<164<169,144 \lt 164 \lt 169, the value 164\sqrt{164} lies between 1212 and 13.13.
Thus, the correct answer is E .
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