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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...)
(No difference)

Revision as of 16:35, 16 April 2009

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 Problems

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