1988 AJHSME Problems/Problem 11

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 $\sqrt{144}<\sqrt{164}<\sqrt{169} \Rightarrow 12<\sqrt{164}<13 \rightarrow \boxed{\text{E}}$

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1988 AJHSME Problems/Problem 11

Problem

Solution

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