Well, for example: I know that $\sqrt{7}$ is a constructible number. Also $\sqrt[\leftroot{-1}\uproot{2}\scriptstyle 3]{2}$ is not a constructible number.
My question is that the product of $\sqrt{7}$ and $\sqrt[\leftroot{-1}\uproot{2}\scriptstyle 3]{2}$ denotes as $\sqrt{7} \cdot \sqrt[\leftroot{-1}\uproot{2}\scriptstyle 3]{2}$ a constructible number or not ?
My guess is $\sqrt{7} \cdot \sqrt[\leftroot{-1}\uproot{2}\scriptstyle 3]{2}$ is not a constructible but I am not sure if my guess is correct
