1957 AHSME Problems/Problem 13: Difference between revisions
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== Problem == | |||
<math>\boxed{C}</math> | A rational number between <math>\sqrt{2}</math> and <math>\sqrt{3}</math> is: | ||
<math>\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 </math> | |||
== Solution == | |||
We see that <math>A</math> and <math>B</math> are both irrational, so we look at <math>C</math>, <math>D</math>, and <math>E</math>. | |||
Recall that <math>\sqrt 2</math> is around <math>1.4</math>, and <math>\sqrt{3}</math> is around <math>1.7</math>. | |||
The only number between these is <math>\boxed{\textbf{(C) }1.5}</math>. | |||
~JustinLee2017 | ~JustinLee2017 | ||
==See Also== | |||
{{AHSME 50p box|year=1957|num-b=12|num-a=14}} | |||
{{MAA Notice}} | |||
[[Category:AHSME]][[Category:AHSME Problems]] | |||
Latest revision as of 08:20, 25 July 2024
Problem
A rational number between 
and 
is:
Solution
We see that 
and 
are both irrational, so we look at 
, 
, and 
.
Recall that 
is around 
, and is around 
.
The only number between these is 
.
~JustinLee2017
See Also
| 1957 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
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| All AHSME Problems and Solutions | ||
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