1957 AHSME Problems/Problem 13

Problem

A rational number between $\sqrt{2}$ and $\sqrt{3}$ is:

$\textbf{(A)}\ \frac{\sqrt{2} + \sqrt{3}}{2} \qquad \textbf{(B)}\ \frac{\sqrt{2} \cdot \sqrt{3}}{2}\qquad \textbf{(C)}\ 1.5\qquad \textbf{(D)}\ 1.8\qquad \textbf{(E)}\ 1.4$

Solution

We see that $A$ and $B$ are both irrational, so we look at $C$ , $D$ , and $E$ . Recall that $\sqrt 2$ is around $1.4$ , and $\sqrt{3}$ is around $1.7$ The only number between these is $\boxed{\textbf{(C) }1.5}$ .

~JustinLee2017

1957 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
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1957 AHSME Problems/Problem 13

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