Question 167
Reduce the following expression into the form $a + b\sqrt{2}$, where both $a$ and $b$ are rational numbers:
$$
\frac{(1 \times 4 + \sqrt{2})(2 \times 5 + \sqrt{2})\cdots(10 \times 13 + \sqrt{2})}{(2 \times 2 - 2)(3 \times 3 - 2)\cdots(11 \times 11 - 2)}
$$
$$
\frac{(1 \times 4 + \sqrt{2})(2 \times 5 + \sqrt{2})\cdots(10 \times 13 + \sqrt{2})}{(2 \times 2 - 2)(3 \times 3 - 2)\cdots(11 \times 11 - 2)}
$$