1989 AMC 12 Problem 2

Attempt Problem 2 of the 1989 AMC 12 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 1989 AMC 12 solutions, or check the answer key.

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

2.

19+116=\sqrt{\frac19+\frac1{16}}=
15\frac15
14\frac14
27\frac27
512\frac5{12}
712\frac7{12}
Answer: D
Concepts:fractionradical
Small hint:
Add the fractions before taking the square root
Big hint:
Use 144144 as a common denominator
Solution:
We have 19+116=16+9144=25144.\frac19+\frac1{16}=\frac{16+9}{144}=\frac{25}{144}. Its positive square root is 512.\frac5{12}.
Thus the correct answer is D.
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