Chapter 9 - Roots and Radicals - 9.2 - Simplifying Radicals - Problem Set 9.2 - Page 407: 55

$3\sqrt{5}$

Using the properties of radicals, the given expression, $ 4\sqrt{45}-9\sqrt{5} ,$ simplifies to \begin{array}{l}\require{cancel} 4\sqrt{9\cdot5}-9\sqrt{5} \\\\= 4\sqrt{(3)^2\cdot5}-9\sqrt{5} \\\\= 4\cdot3\sqrt{5}-9\sqrt{5} \\\\= 12\sqrt{5}-9\sqrt{5} \\\\= 3\sqrt{5} .\end{array}