The diagonal of a square is $$4\sqrt 2 $$ cm. The diagonal of another square whose area is double that of the first square, is :

$$\eqalign{ & d = 4\sqrt 2 \,cm \cr & \Rightarrow {\text{Area }} = \frac{1}{2}d_1^2 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2} \times {\left( {4\sqrt 2 } \right)^2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 16}}\,{\text{c}}{{\text{m}}^2} \cr} $$
Area of new square = (2 × 16) cm² = 32 cm²
$$\eqalign{ & \therefore \frac{1}{2}d_2^2 = 32 \cr & \Rightarrow d_2^2 = 64 \cr & \Rightarrow {d_2} = 8\,cm \cr} $$