Difference between revisions of "1988 AJHSME Problems/Problem 11"

(New page: ==Problem== <math>\sqrt{164}</math> is <math>\text{(A)}\ 42 \qquad \text{(B)}\ \text{less than }10 \qquad \text{(C)}\ \text{between }10\text{ and }11 \qquad \text{(D)}\ \text{between }1...)
 
 
(One intermediate revision by one other user not shown)
Line 13: Line 13:
 
==See Also==
 
==See Also==
  
[[1988 AJHSME Problems]]
+
{{AJHSME box|year=1988|num-b=10|num-a=12}}
 +
[[Category:Introductory Algebra Problems]]
 +
{{MAA Notice}}

Latest revision as of 23:55, 4 July 2013

Problem

$\sqrt{164}$ is

$\text{(A)}\ 42 \qquad \text{(B)}\ \text{less than }10 \qquad \text{(C)}\ \text{between }10\text{ and }11 \qquad \text{(D)}\ \text{between }11\text{ and }12 \qquad \text{(E)}\ \text{between }12\text{ and }13$

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 (ProblemsAnswer KeyResources)
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
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png