Chapter 10 - Radical Expressions and Equations - 10-3 Operations With Radical Expressions - Practice and Problem-Solving Exercises - Page 629: 14

$47 \sqrt 2$

You are given $4\sqrt 128$ $+$ $5\sqrt 18$.Simplify: Factor perfect squares out of the radicans: $4 \sqrt 64*2$ $+$ $5 \sqrt 9*2$ Multiplication property: $4 (\sqrt 64) ({\sqrt 2})$ $+$ $5 (\sqrt 9) ({\sqrt 2})$ $4(8) (\sqrt 2)$ $+$ $5(3) (\sqrt 2)$ $32\sqrt 2$ $+$ $15\sqrt 2$ $\sqrt 2(32+15)$ =$47\sqrt 2$