Irrational Numbers Math Example 2

Solution

1. 1
   Compute $1.4^2 = 1.96$ and $1.5^2 = 2.25$.
2. 2
   Since $1.96 < 2 < 2.25$, we have $1.4 < \sqrt{2} < 1.5$.
3. 3
   Try $1.41^2 = 1.9881$ and $1.42^2 = 2.0164$. Since $1.9881 < 2 < 2.0164$, $\sqrt{2} \approx 1.4$ to one decimal place.