Write the following in terms of i and simplify. V- 25 81

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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## Exercise Example: Simplifying with Imaginary Numbers

### Example 3: 
**KAUFIALG10 6.1.031**

Consider the following example:

\[
\sqrt{-20} = i\sqrt{20} = i\sqrt{4}\sqrt{5} = 2i\sqrt{5}
\]

**Task:** Write the following in terms of \( i \) and simplify.

\[
\sqrt{\frac{25}{81}}
\]

*Solution Box:* [ ]

*Submit Answer Button*

---

### Example 4:
**KAUFIALG10 6.1.033**

Consider the following example:

\[
\sqrt{-20} = i\sqrt{20} = i\sqrt{4}\sqrt{5} = 2i\sqrt{5}
\]

**Task:** Write the following in terms of \( i \) and simplify.

\[
\sqrt{-20}
\]

*Solution Box:* [ ]

*Submit Answer Button*

---

### Instructions:
For both examples, follow the steps outlined in the provided example to express the given square roots in terms of the imaginary unit \( i \). Remember, \( i = \sqrt{-1} \), so you will need to separate negative numbers from the square roots.
Transcribed Image Text:## Exercise Example: Simplifying with Imaginary Numbers ### Example 3: **KAUFIALG10 6.1.031** Consider the following example: \[ \sqrt{-20} = i\sqrt{20} = i\sqrt{4}\sqrt{5} = 2i\sqrt{5} \] **Task:** Write the following in terms of \( i \) and simplify. \[ \sqrt{\frac{25}{81}} \] *Solution Box:* [ ] *Submit Answer Button* --- ### Example 4: **KAUFIALG10 6.1.033** Consider the following example: \[ \sqrt{-20} = i\sqrt{20} = i\sqrt{4}\sqrt{5} = 2i\sqrt{5} \] **Task:** Write the following in terms of \( i \) and simplify. \[ \sqrt{-20} \] *Solution Box:* [ ] *Submit Answer Button* --- ### Instructions: For both examples, follow the steps outlined in the provided example to express the given square roots in terms of the imaginary unit \( i \). Remember, \( i = \sqrt{-1} \), so you will need to separate negative numbers from the square roots.
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