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}}}\quad
+
<math>\text{(A) } \sqrt{\sqrt[3]{5\cdot 6}}\quad
\text{(B) } \sqrt{6\sqrt[3]{5}}}\quad
+
\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>
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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?

$\text{(A) } \sqrt{\sqrt[3]{5\cdot 6}}\quad \text{(B) } \sqrt{6\sqrt[3]{5}}\quad \text{(C) } \sqrt{5\sqrt[3]{6}}\quad \text{(D) } \sqrt[3]{5\sqrt{6}}\quad \text{(E) } \sqrt[3]{6\sqrt{5}}$

Solution

Putting them all in the form $\sqrt{\sqrt[3]N}$ (the order of the radicals doesn't matter), the resulting interior numbers are \[30, 1080, 750, 150, 180\] so the answer is $\fbox{B}$

See also

1990 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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