Ta có: \(\left( {\overrightarrow a + 3\overrightarrow b } \right) \cdot \left( {\overrightarrow a - 2\overrightarrow b } \right)\)

\( = {\overrightarrow a ^2} - 6{\overrightarrow b ^2} + \overrightarrow a \cdot \overrightarrow b \)

\( = {1^2} - 6 \cdot {1^2} + 1 \cdot 1 \cdot \cos 45^\circ \)

\[ = - 5 + \frac{{\sqrt 2 }}{2} \approx - 4,3\].

Đáp số: \( - 4,3\).