1973 AHSME Problems/Problem 13
Revision as of 16:31, 27 July 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 13 (credit to gaussintraining))
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
![\[\sqrt{(\frac{2(\sqrt2+\sqrt6)}{3\sqrt{2+\sqrt3}})^2}\]](http://latex.artofproblemsolving.com/7/d/7/7d7e82c4784c8cc14b702ac3930f11c05691efdb.png)
![\[\sqrt{\frac{4(2+4\sqrt{3}+6)}{9(2+\sqrt{3}}}\]](http://latex.artofproblemsolving.com/7/e/7/7e7e030d6b6573a8f6f962cf0b188506770ef0ed.png)
![\[\sqrt{\frac{4(8+4\sqrt{3})}{9(2+\sqrt{3}}}\]](http://latex.artofproblemsolving.com/e/9/c/e9cf224aee6586344617afce8008d193d7ee6efa.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 | ||
