Chapter 7 - Exponential and Logarithmic Functions - 7-2 Properties of Exponential Functions - Practice and Problem-Solving Exercises - Page 450: 58

$\sqrt3$

Simplify each radical to obtain: \begin{align*} &=5\sqrt{3}-2\sqrt{4(3)}\\ &=5\sqrt{3}-2\sqrt{2^2(3)}\\ &=5\sqrt3-2(2)\sqrt3\\ &=5\sqrt3-4\sqrt3 \end{align*} Recall: For any real numbers $a, b, $ and $c$, $$a(b+c)=ab+ac$$ Use the rule above to obtain: \begin{align*} 5\sqrt{3}-4\sqrt{3}&=(5-4)\sqrt{3}\\ &=1\sqrt{3}\\ &=\sqrt{3} \end{align*}