To find the simplified form, we need to determine the given expression. However, it seems like the question has some formatting issues, making it unclear what exactly needs simplifying.
Let's take each option and simplify it as much as possible:
1. \( 4n^3 \sqrt{3} \)
2. \( 4n^4 \sqrt{3n} \)
3. \( 3n \sqrt{4n^8} \)
4. \( 4 \sqrt{3n^9} \)
Let's simplify these expressions one by one:
1. \( 4n^3 \sqrt{3} \):
- This expression is already in its simplest form: \( 4n^3 \sqrt{3} \).
2. \( 4n^4 \sqrt{3n} \):
- This can be written as \( 4n^4 \sqrt{3n} \).
- Since \( \sqrt{3n} = \sqrt{3} \cdot \sqrt{n} \), the expression becomes \( 4n^4 \cdot \sqrt{3} \cdot \sqrt{n} \).
- Combine the terms to get \( 4n^4 \sqrt{3n} \).
3. \( 3n \sqrt{4n^8} \):
- First, simplify the part inside the square root: \( \sqrt{4n^8} = \sqrt{4} \cdot \sqrt{n^8} = 2n^4 \).
- Substituting this back, we get \( 3n \cdot 2n^4 = 6n^5 \).
4. \( 4 \sqrt{3n^9} \):
- Simplify the part inside the square root: \( \sqrt{3n^9} = \sqrt{3} \cdot \sqrt{n^9} = \sqrt{3} \cdot n^{9/2} = \sqrt{3} \cdot n^{4.5} \).
- Combining this back, we get \( 4 \cdot \sqrt{3} \cdot n^{4.5} \).
The simplest forms of the given expressions are:
1. \( 4n^3 \sqrt{3} \)
2. \( 4n^4 \sqrt{3n} \)
3. \( 6n^5 \)
4. \( 4 \sqrt{3} n^{4.5} \)
Now assuming we're comparing to find the simplest individual form (or assuming the original prompt was asking which of these simplifications is accurate):
- \( 4n^4 \sqrt{3n} \) progresses in simplified form from \( 4 \sqrt{3n^9} \).
Therefore, if your original expression simplifies directly to one, the answer should be "4n^4 √3n."
However, given the question isn't exactly clear, we should choose based on assumptions that might align better with your provided alternatives. Thus, the answer might depend on context not visible here, but from given, this should fit closest soured elements degree matching integration of expression:
Given original as \( 4 \sqrt{3n^9} \).
The simplified form appears as:
**4 \sqrt{3n^9} = 4 \sqrt3 n^4.5 (rounded)**.
Your earlier aligned simplest form fits given \(2)\ fourth properly.
Question What is the simplified form of ? (1 point) Responses Image with alt text: 4 n cubed Start Root 3 End Root Image with alt text: 4 n superscript 4 baseline Start Root 3 n End Root Image with alt text: 3 n Start Root 4 n superscript 8 baseline End Root Image with alt text: 4 Start Root 3 n superscript 9 baseline End Root
1 answer