Question

In the following exercises, write each expression in terms of i and simplify if possible.$$\begin{gathered} a\left)\sqrt{-16} \\ b\right)\sqrt{-11} \\ c)\sqrt{-8} \end{gathered}$$

Short answer

The simplified expression are

$$\begin{gathered} a\left)4i \\ b\right)\sqrt{11}i \\ c)2\sqrt{2}i \end{gathered}$$

Step-by-step solution

Part (a) Step 1: Given information

We are given an expression$\sqrt{-16}$

Part(a) Step 2: Use the definition of the square root of a negative number

We get,$\sqrt{16}i$

Part (a) Step 3: Simplify

On simplifying we get,$4i$

Part (b) Step 1: Given information

We are given an expression$\sqrt{-11}$

Part (b) Step 2: Use the definition of the square root of negative number

We get,$\sqrt{11}i$

Part (b) Step 3: Simplify

On simplifying we get$\sqrt{11}i$

Part (c) Step 1: Given information

We are given an expression$\sqrt{-8}$

Part(c) Step 2: Use the definition of the square root of negative number

We get,$\sqrt{8}i$

Part (c) Step 3: Simplify

On simplifying we get,$2\sqrt{2}i$

Conclusion

The simplifies expression can be given as

$$\begin{gathered} a\left)4i \\ b\right)\sqrt{11}i \\ c)2\sqrt{2}i \end{gathered}$$