<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:
$$\color{blue}8-\color{red}{2\sqrt{18}}=\color{blue}{\sqrt{64}}-\color{red}{\sqrt{4}\sqrt{18}}=\color{blue}{\sqrt{64}}-\color{red}{\sqrt{72}}$$
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