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Difference between revisions of "1975 AHSME Problems/Problem 29"

(Created page with "==Problem== What is the smallest integer larger than <math>(\sqrt{3}+\sqrt{2})^6</math>? <math>\textbf{(A)}\ 972 \qquad \textbf{(B)}\ 971 \qquad \textbf{(C)}\ 970 \qquad \te...")
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Revision as of 03:13, 25 June 2019

Problem

What is the smallest integer larger than $(\sqrt{3}+\sqrt{2})^6$?

$\textbf{(A)}\ 972 \qquad \textbf{(B)}\ 971 \qquad \textbf{(C)}\ 970 \qquad \textbf{(D)}\ 969 \qquad \textbf{(E)}\ 968$

Solution

$(\sqrt{3}+\sqrt{2})^6=(5+2\sqrt{6})^3=(5+2\sqrt{6})(31+20\sqrt{6})=(395+162\sqrt{6})$

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