Answer
Not linear.
Work Step by Step
In this case the transformation is linear if $T(v_1+v_2)=T(v_1)+T(v_2)$ and $T(av_1)=aT(v_1)$ for any $v_1,v_2$ in the domain and any $a$ scalar.
Here this is violated because e.g. $T(1,1)=(1,1,1)$ but $T((1,1)+(1,1))=T(2,2)=(\sqrt2,4,\sqrt2)\ne(2,2,2)=(1,1,1)+(1,1,1)=T(1,1,+T(1,1).$