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AHSME 1950 Problem 10

    After rationalizing the numerator of 3−23\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}}, the denominator in simplest form is: (A) 3(3+2)(B) 3(3−2)(C) 3−32(D) 3+6(E) None of these answers\textbf{(A)}\ \sqrt{3}(\sqrt{3}+\sqrt{2}) \textbf{(B)}\ \sqrt{3}(\sqrt{3}-\sqrt{2}) \textbf{(C)}\ 3-\sqrt{3}\sqrt{2} \\ \textbf{(D)}\ 3+\sqrt6 \textbf{(E)}\ \text{None of these answers}

    Dataset text NuminaMath-1.5. Quoted with source.

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    3+\sqrt{6}

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