Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set - Page 585: 41

$6y^{50}\sqrt{2}$

Getting the perfect factors and then extracting its root, the simplified form of the given expression, $ \sqrt{72y^{100}} ,$ is \begin{array}{l}\require{cancel} \sqrt{36y^{100}\cdot2} \\\\= \sqrt{(6y^{50})^2\cdot2} \\\\= 6y^{50}\sqrt{2} .\end{array}