1988 AJHSME Problems/Problem 11

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Problem

$\sqrt{164}$ is

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

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

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