2根号2，即$\sqrt{2}$，是一个无理数，也就是说它不能表示为两个整数的比值。我们可以通过一些方法来近似地化简这个表达式。
1. 使用泰勒级数展开
$\sqrt{2}$ 可以近似地用泰勒级数展开来表示：
$$\sqrt{2} \approx 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt{2}) = 1 + \frac{1}{2}(1 – \sqrt