Question

In the following exercises, simplify using absolute value signs as needed.

$$\begin{gathered} \left(a\right)8+\sqrt{96} \\ \left(b\right)\frac{2+\sqrt{40}}{2} \end{gathered}$$

Short answer

The required answers are$8+4\sqrt{6}and1+\sqrt{10}$

Step-by-step solution

Step 1. Given Information

The given expressions are

$$\begin{gathered} \left(a\right)8+\sqrt{96} \\ \left(b\right)\frac{2+\sqrt{40}}{2} \end{gathered}$$

Part(a) Step 1. Calculation

Simplify the expression by rewriting the radical using product property.

$$\begin{gathered} 8+\sqrt{96}=8+\sqrt{16\times 6} \\ =8+4\sqrt{6} \end{gathered}$$

Part(b) Step 1. Calculation

Simplify the expression by rewriting the radical using product property.

$$\begin{gathered} \frac{2+\sqrt{40}}{2}=\frac{2+\sqrt{4\times 10}}{2} \\ =\frac{2+2\sqrt{10}}{2} \\ =1+\sqrt{10} \end{gathered}$$