Difference between revisions of "1990 AHSME Problems/Problem 5"
(Created page with "== Problem == Which of these numbers is largest? <math>\text{(A) } \sqrt{\sqrt[3]{5\cdot 6}}}\quad \text{(B) } \sqrt{6\sqrt[3]{5}}}\quad \text{(C) } \sqrt{5\sqrt[3]{6}}\quad \te...") |
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Which of these numbers is largest? | Which of these numbers is largest? | ||
| − | <math>\text{(A) } \sqrt{\sqrt[3]{5\cdot 6 | + | <math>\text{(A) } \sqrt{\sqrt[3]{5\cdot 6}}\quad |
| − | \text{(B) } \sqrt{6\sqrt[3]{5 | + | \text{(B) } \sqrt{6\sqrt[3]{5}}\quad |
\text{(C) } \sqrt{5\sqrt[3]{6}}\quad | \text{(C) } \sqrt{5\sqrt[3]{6}}\quad | ||
\text{(D) } \sqrt[3]{5\sqrt{6}}\quad | \text{(D) } \sqrt[3]{5\sqrt{6}}\quad | ||
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== Solution == | == Solution == | ||
| − | <math>\fbox{B}</math> | + | Putting them all in the form <math>\sqrt{\sqrt[3]N}</math> (the order of the radicals doesn't matter), the resulting interior numbers are <cmath>30, 1080, 750, 150, 180</cmath> so the answer is <math>\fbox{B}</math> |
== See also == | == See also == | ||
Latest revision as of 03:05, 4 February 2016
Problem
Which of these numbers is largest?
![$\text{(A) } \sqrt{\sqrt[3]{5\cdot 6}}\quad \text{(B) } \sqrt{6\sqrt[3]{5}}\quad \text{(C) } \sqrt{5\sqrt[3]{6}}\quad \text{(D) } \sqrt[3]{5\sqrt{6}}\quad \text{(E) } \sqrt[3]{6\sqrt{5}}$](http://latex.artofproblemsolving.com/4/e/c/4ece344cb471dfcda996465510d9920eaf36d9e9.png)
Solution
Putting them all in the form ![$\sqrt{\sqrt[3]N}$](http://latex.artofproblemsolving.com/1/f/b/1fbfbf812c1945bd986d1e09fd9a36828db9956c.png)
(the order of the radicals doesn't matter), the resulting interior numbers are ![\[30, 1080, 750, 150, 180\]](http://latex.artofproblemsolving.com/3/f/6/3f65df17b6de5e29b6df29cc64f461cb828a8302.png)
so the answer is 
See also
| 1990 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
