Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 47

$12a\sqrt[]{b}$

Using the properties of radicals, the given expression, $ (4\sqrt[]{a})(3\sqrt[]{ab}) ,$ simplifies to \begin{array}{l} 4(3)\sqrt[]{a(ab)} \\\\= 12\sqrt[]{a^2b} \\\\= 12\sqrt[]{(a)^2\cdot b} \\\\= 12\cdot a\sqrt[]{b} \\\\= 12a\sqrt[]{b} .\end{array}