Chapter 4 - Quadratic Functions and Equations - Square Roots and Radicals - Exercises - Page 225: 9

$$108$$

Recall: (1) $\left(\sqrt{a}\right)^2=|a|$ (2) $(ab)^m=a^mb^m$ Using rule (2) above gives: \begin{align*} \left(2\sqrt{27}\right)^2&=2^2 \cdot \left(\sqrt{27}\right)^2\\ &=4\left(\sqrt{27}\right)^2 \end{align*} Using rule (1) above gives: \begin{align*} 4\left(\sqrt{27}\right)^2&=4(|27|)\\ &=4(27)\\ &=108 \end{align*}