Show which of $6-2\sqrt{3}$ and $3\sqrt{2}-2$ is greater without using calculator How do you compare $6-2\sqrt{3}$ and $3\sqrt{2}-2$? (no calculator)
Look simple but I have tried many ways and fail miserably.
Both are positive, so we cannot find which one is bigger than $0$ and the other smaller than $0$.
Taking the first minus the second in order to see the result positive or negative get me no where (perhaps I am too dense to see through).

$$
6-2√3 \sim 3√2-2\\
8 \sim 3√2 +2√3 \\
64 \sim 30+12√6\\
34 \sim 12√6\\
17 \sim 6√6\\
289 \sim 36 \cdot 6\\
289 > 216
$$
