Is it possible to use
**
exactly three
**
$\sqrt{2}$
's and
**
no multiplication signs
**
to get 2?

Example : It is possible to get $3 \times \sqrt{2}$ by simply adding the $\sqrt{2}$ 's together. It is also possible to get $\sqrt{2}$ by $( \sqrt{2} + \sqrt{2} - \sqrt{2})$ .

No
Yes

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There are multiple ways to achieve this. The most obvious is $\frac{\sqrt{2} + \sqrt{2} }{ \sqrt{2} }$ . Another is $(\sqrt{2}^{\sqrt{2}})^{\sqrt{2}}$ . So the answer is obviously Yes.