2003 AMC 10A Problems/Problem 9: Difference between revisions
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== See Also == | == See Also == | ||
{{AMC10 box|year=2003|ab=A|num-b=8|num-a=10}} | |||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
![$\sqrt[3]{x\sqrt[3]{x\sqrt[3]{x\sqrt{x}}}}$](http://latex.artofproblemsolving.com/c/f/2/cf2756b7e9bb76b2adf76f1709cc765535b27602.png)
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![$\mathrm{(A) \ } \sqrt{x}\qquad \mathrm{(B) \ } \sqrt[3]{x^{2}}\qquad \mathrm{(C) \ } \sqrt[27]{x^{2}}\qquad \mathrm{(D) \ } \sqrt[54]{x}\qquad \mathrm{(E) \ } \sqrt[81]{x^{80}}$](http://latex.artofproblemsolving.com/2/e/1/2e12822d4d418ef37b7ca03cff39d5b6e8123508.png)
![$\sqrt[3]{x\sqrt{x}}=\sqrt[3]{(\sqrt{x})^{2}\cdot\sqrt{x}}=\sqrt[3]{(\sqrt{x})^{3}}=\sqrt{x}$](http://latex.artofproblemsolving.com/5/b/5/5b532d915bdc855d96cfa266d7d3bb9a168fd803.png)
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![$\sqrt[3]{x\sqrt[3]{x\sqrt[3]{x\sqrt{x}}}}=\sqrt[3]{x\sqrt[3]{x\sqrt{x}}}=\sqrt[3]{x\sqrt{x}}= \sqrt{x} \Rightarrow A$](http://latex.artofproblemsolving.com/b/d/9/bd94c3e0a7fb90973d3de1b2b1e986027f8c7a45.png)
