Question

question 2:
simplify the radical expression shown below by adding and/or subtracting
2\sqrt3{2}+5\sqrt3{16}
question 3:
determine the perimeter of the triangle.

Explanation:

Step1: Simplify the radical

$$\begin{align*} 5\sqrt[3]{16}&=5\sqrt[3]{8\times2}\\ &=5\sqrt[3]{8}\times\sqrt[3]{2}\\ &=5\times2\times\sqrt[3]{2}\\ & = 10\sqrt[3]{2} \end{align*}$$

Step2: Combine like terms

$$\begin{align*} 2\sqrt[3]{2}+5\sqrt[3]{16}&=2\sqrt[3]{2}+10\sqrt[3]{2}\\ &=(2 + 10)\sqrt[3]{2}\\ &=12\sqrt[3]{2} \end{align*}$$

Answer:

$12\sqrt[3]{2}$