In Chapter 2, when we defined square roots, we introduced Heron’s method, a first-century algorithm to compute √ x given x. See p. 218, or Figure 4.20 for a reminder. Here you’ll prove two properties...

In Chapter 2, when we defined square roots, we introduced Heron’s method, a first-century algorithm to compute √ x given x. See p. 218, or Figure 4.20 for a reminder. Here you’ll prove two properties that help establish why this algorithm correctly computes square roots:

Figure 4.20: A reminder of Heron’s method for computing square root