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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<math>\textbf{(A)}\ 972 \qquad \textbf{(B)}\ 971 \qquad \textbf{(C)}\ 970 \qquad \textbf{(D)}\ 969 \qquad \textbf{(E)}\ 968</math> | <math>\textbf{(A)}\ 972 \qquad \textbf{(B)}\ 971 \qquad \textbf{(C)}\ 970 \qquad \textbf{(D)}\ 969 \qquad \textbf{(E)}\ 968</math> | ||
| − | ==Solution== | + | ==Solution(Very Stupid)== |
| − | <math>(\sqrt{3}+\sqrt{2})^6=(5+2\sqrt{6})^3=(5+2\sqrt{6})(31+20\sqrt{6})=(395+162\sqrt{6})</math> | + | <math>(\sqrt{3}+\sqrt{2})^6=(5+2\sqrt{6})^3=(5+2\sqrt{6})(31+20\sqrt{6})=(395+162\sqrt{6})</math> Then, find that <math>\sqrt{6}</math> is about <math>2.449</math>. Finally, multiply and add to find that the smallest integer higher is <math>\boxed {\textbf{(A) } 972}</math> |
Revision as of 03:29, 25 June 2019
Problem
What is the smallest integer larger than 
?
Solution(Very Stupid)
Then, find that 
is about 
. Finally, multiply and add to find that the smallest integer higher is 
