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1988 AJHSME Problems/Problem 11

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Problem

$\sqrt{164}$ is

$\text{(A)}\ 42 \qquad \text{(B)}\ \text{less than }10 \qquad \text{(C)}\ \text{between }10\text{ and }11 \qquad \text{(D)}\ \...$

Solution

Note that if $1\leq a<b<c$ , then $\sqrt{a}<\sqrt{b}<\sqrt{c}$ .

Since $1<144<164<169$ , we can say that $\sqrt{144}<\sqrt{164}<\sqrt{169} \Rightarrow 12<\sqrt{164}<13 \rightarrow \boxed{\text{E}}$

See Also

1988 AJHSME (Problems • Resources)
Preceded by Problem 10	Followed by Problem 12
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/1988_AJHSME_Problems/Problem_11"

Category: Introductory Algebra Problems

Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.

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