Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set - Page 585: 42

$4y^{100}\sqrt{2}$

Getting the perfect factors and then extracting its root, the simplified form of the given expression, $ \sqrt{32y^{200}} ,$ is \begin{array}{l}\require{cancel} \sqrt{16y^{200}\cdot2} \\\\= \sqrt{(4y^{100})^2\cdot2} \\\\= 4y^{100}\sqrt{2} .\end{array}