Difference between revisions of "1973 AHSME Problems/Problem 13"
Rockmanex3 (talk | contribs) (Solution to Problem 13 (credit to gaussintraining)) |
Rockmanex3 (talk | contribs) m (→Solution) |
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Squaring the expression and taking the positive square root (since numerator and denominator are positive) of the result yields | Squaring the expression and taking the positive square root (since numerator and denominator are positive) of the result yields | ||
| − | <cmath>\sqrt{(\frac{2(\sqrt2+\sqrt6)}{3\sqrt{2+\sqrt3}})^2}</cmath> | + | <cmath>\sqrt{\left(\frac{2(\sqrt2+\sqrt6)}{3\sqrt{2+\sqrt3}}\right)^2}</cmath> |
| − | <cmath>\sqrt{\frac{4(2+4\sqrt{3}+6)}{9(2+\sqrt{3}}}</cmath> | + | <cmath>\sqrt{\frac{4(2+4\sqrt{3}+6)}{9(2+\sqrt{3})}}</cmath> |
| − | <cmath>\sqrt{\frac{4(8+4\sqrt{3})}{9(2+\sqrt{3}}}</cmath> | + | <cmath>\sqrt{\frac{4(8+4\sqrt{3})}{9(2+\sqrt{3})}}</cmath> |
<cmath>\sqrt{\frac{16}{9}}</cmath> | <cmath>\sqrt{\frac{16}{9}}</cmath> | ||
<cmath>\frac43</cmath> | <cmath>\frac43</cmath> | ||
Revision as of 17:32, 27 July 2018
Problem
The fraction 
is equal to
Solution
Squaring the expression and taking the positive square root (since numerator and denominator are positive) of the result yields
![\[\sqrt{\left(\frac{2(\sqrt2+\sqrt6)}{3\sqrt{2+\sqrt3}}\right)^2}\]](http://latex.artofproblemsolving.com/d/5/6/d56ac6e977e206d9166fac39bd65d2df75e7eb47.png)
![\[\sqrt{\frac{4(2+4\sqrt{3}+6)}{9(2+\sqrt{3})}}\]](http://latex.artofproblemsolving.com/a/2/8/a28c8989a373501f35847bb2d5fd99d2fc2c71e3.png)
![\[\sqrt{\frac{4(8+4\sqrt{3})}{9(2+\sqrt{3})}}\]](http://latex.artofproblemsolving.com/f/f/f/ffffc853cccb7e9a99220d4cbdd88d3e563f321e.png)
![\[\sqrt{\frac{16}{9}}\]](http://latex.artofproblemsolving.com/8/b/0/8b0e8b55c0c2baabf8d7eeffe2a5524a7617aef3.png)
![\[\frac43\]](http://latex.artofproblemsolving.com/e/2/3/e23678da45f8dc2e1bf4726e4121044934b7b6bf.png)
The answer is 
.
See Also
| 1973 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 | ||
| All AHSME Problems and Solutions | ||
