1957 AHSME Problems/Problem 13: Difference between revisions

Latest revision as of 08:20, 25 July 2024

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
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

@@ Line 9: / Line 9: @@
 \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,</math> and <math>E</math>
+== Solution ==
-Recall that <math>\sqrt 2</math> is around <math>1.414</math>, and <math>\sqrt{3}</math> is around <math>1.732</math>
-So the only number between that is <math>\boxed{\textbf{(C) }1.5}</math>.
+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

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1957 AHSME Problems/Problem 13: Difference between revisions

Latest revision as of 08:20, 25 July 2024

Problem

Solution

See Also