<s>[INST] Which is bigger, $1+3\sqrt{2}$ or $3\sqrt{3}$? Which is bigger, $a = 1+3\sqrt2$ or $b = 3\sqrt3$?
To find out result, I am doing: $(3\sqrt3)^2-(1+3\sqrt2)^2=8-2\sqrt{18}$.
But how can I find if the value of $8-2\sqrt{18}$ is positive or negative?
Thank you.
 [/INST] HINT:
Note that $(3\sqrt3)^2-(1+3\sqrt2)^2=27-1-6\sqrt2-18=8-6\sqrt2$. Next note that $\sqrt2>\frac86$.
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