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Difference between revisions of "1962 AHSME Problems/Problem 2"

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==Solution==
 
==Solution==
 
Simplifying <math>\sqrt{\dfrac{4}{3}}</math> yields <math>\dfrac{2}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}</math>.
 
Simplifying <math>\sqrt{\dfrac{4}{3}}</math> yields <math>\dfrac{2}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}</math>.
 +
  
 
Simplifying <math>\sqrt{\dfrac{3}{4}}</math> yields <math>\dfrac{\sqrt{3}}{2}</math>.
 
Simplifying <math>\sqrt{\dfrac{3}{4}}</math> yields <math>\dfrac{\sqrt{3}}{2}</math>.
 +
  
 
<math>\dfrac{2\sqrt{3}}{3}-\dfrac{\sqrt{3}}{2}=\dfrac{4\sqrt{3}}{6}-\dfrac{3\sqrt{3}}{6}=\dfrac{\sqrt{3}}{6}</math>.
 
<math>\dfrac{2\sqrt{3}}{3}-\dfrac{\sqrt{3}}{2}=\dfrac{4\sqrt{3}}{6}-\dfrac{3\sqrt{3}}{6}=\dfrac{\sqrt{3}}{6}</math>.
 +
  
 
Since we cannot simplify further, the correct answer is <math>\textbf{(A)}\ \frac{\sqrt{3}}{6}\qquad</math>
 
Since we cannot simplify further, the correct answer is <math>\textbf{(A)}\ \frac{\sqrt{3}}{6}\qquad</math>

Revision as of 23:48, 9 November 2013

Problem

The expression $\sqrt{\frac{4}{3}} - \sqrt{\frac{3}{4}$ (Error compiling LaTeX. Unknown error_msg) is equal to:

$\textbf{(A)}\ \frac{\sqrt{3}}{6}\qquad\textbf{(B)}\ \frac{-\sqrt{3}}{6}\qquad\textbf{(C)}\ \frac{\sqrt{-3}}{6}\qquad\textbf{(D)}\ \frac{5\sqrt{3}}{6}\qquad\textbf{(E)}\ 1$

Solution

Simplifying $\sqrt{\dfrac{4}{3}}$ yields $\dfrac{2}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}$.


Simplifying $\sqrt{\dfrac{3}{4}}$ yields $\dfrac{\sqrt{3}}{2}$.


$\dfrac{2\sqrt{3}}{3}-\dfrac{\sqrt{3}}{2}=\dfrac{4\sqrt{3}}{6}-\dfrac{3\sqrt{3}}{6}=\dfrac{\sqrt{3}}{6}$.


Since we cannot simplify further, the correct answer is $\textbf{(A)}\ \frac{\sqrt{3}}{6}\qquad$

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