Difference between revisions of "2008 AMC 10B Problems/Problem 3"
I like pie (talk | contribs) (New page: ==Problem== Assume that <math>x</math> is a positive real number. Which is equivalent to <math>\sqrt[3]{x\sqrt{x}}</math>? <math>\mathrm{(A)}\ x^{1/6}\qquad\mathrm{(B)}\ x^{1/4}\q...) |
I like pie (talk | contribs) (Added solution) |
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==Solution== | ==Solution== | ||
| − | {{ | + | <math>\sqrt[3]{x\sqrt{x}}=\sqrt[3]{\sqrt{x^3}}=\sqrt[6]{x^3}=x^{3/6}=x^{1/2}\ \mathrm{(D)}</math> |
==See also== | ==See also== | ||
{{AMC10 box|year=2008|ab=B|num-b=2|num-a=4}} | {{AMC10 box|year=2008|ab=B|num-b=2|num-a=4}} | ||
Revision as of 01:46, 25 April 2008
Problem
Assume that 
is a positive real number. Which is equivalent to ![$\sqrt[3]{x\sqrt{x}}$](http://latex.artofproblemsolving.com/b/b/6/bb6b6aec07627f5fe5db310965f0a81771c5a48e.png)
?
Solution
![$\sqrt[3]{x\sqrt{x}}=\sqrt[3]{\sqrt{x^3}}=\sqrt[6]{x^3}=x^{3/6}=x^{1/2}\ \mathrm{(D)}$](http://latex.artofproblemsolving.com/5/6/d/56dc835e5359449836117a0f73087413e659627b.png)
See also
| 2008 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
