Difference between revisions of "1957 AHSME Problems/Problem 13"
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\textbf{(E)}\ 1.4 </math> | \textbf{(E)}\ 1.4 </math> | ||
| − | We see that <math>A</math> and <math>B</math> are both irrational, so we look at <math>C, D | + | == Solution == |
| − | Recall that <math>\sqrt 2</math> is around <math>1. | + | |
| − | + | 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== | ==See Also== | ||
{{AHSME 50p box|year=1957|num-b=12|num-a=14}} | {{AHSME 50p box|year=1957|num-b=12|num-a=14}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
[[Category:AHSME]][[Category:AHSME Problems]] | [[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 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
