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Original Question
How can you rewrite 36^((1)/(3))using a root?Asked by bluesanta
How can you rewrite 9 1/3
using a root
using a root
Answers
Answered by
GPT-4o mini
To rewrite \( 9 \frac{1}{3} \) using a root, you first need to convert the mixed number into an improper fraction.
1. Convert \( 9 \frac{1}{3} \) to an improper fraction:
\[
9 \frac{1}{3} = \frac{9 \times 3 + 1}{3} = \frac{27 + 1}{3} = \frac{28}{3}
\]
2. Now, to express this fraction using a root, you can manipulate it as follows:
- First, find a way to represent \( 28 \) as a root. You can write \( 28 \) as \( 16 + 12 \), or you can express it more simply.
- Notice that \( 28 \) can be expressed as \( \sqrt{784} \) since \( 784 \) is \( 28^2 \).
Thus, we can rewrite \( \frac{28}{3} \) as:
\[
\frac{\sqrt{784}}{3}
\]
Alternatively, if you're looking for a simpler expression, you can also factor \( 28 \):
\[
28 = 4 \times 7
\]
This means it can also be written as:
\[
\frac{2\sqrt{7}}{3}
\]
However, for a more straightforward expression, the previous form works well.
So, \( 9 \frac{1}{3} \) can be rewritten as:
\[
\frac{\sqrt{784}}{3}
\]
or \(\frac{2\sqrt{7}}{3}\) depending on the context you desire!
1. Convert \( 9 \frac{1}{3} \) to an improper fraction:
\[
9 \frac{1}{3} = \frac{9 \times 3 + 1}{3} = \frac{27 + 1}{3} = \frac{28}{3}
\]
2. Now, to express this fraction using a root, you can manipulate it as follows:
- First, find a way to represent \( 28 \) as a root. You can write \( 28 \) as \( 16 + 12 \), or you can express it more simply.
- Notice that \( 28 \) can be expressed as \( \sqrt{784} \) since \( 784 \) is \( 28^2 \).
Thus, we can rewrite \( \frac{28}{3} \) as:
\[
\frac{\sqrt{784}}{3}
\]
Alternatively, if you're looking for a simpler expression, you can also factor \( 28 \):
\[
28 = 4 \times 7
\]
This means it can also be written as:
\[
\frac{2\sqrt{7}}{3}
\]
However, for a more straightforward expression, the previous form works well.
So, \( 9 \frac{1}{3} \) can be rewritten as:
\[
\frac{\sqrt{784}}{3}
\]
or \(\frac{2\sqrt{7}}{3}\) depending on the context you desire!
Answered by
GPT-4o mini
\( 9 \frac{1}{3} = \frac{\sqrt{784}}{3} \)
Answered by
GPT-4o mini
I apologize for the confusion in my previous response. The correct expression for \( 9 \frac{1}{3} \) is:
\( 9 \frac{1}{3} = \frac{28}{3} \).
The expression \( \frac{\sqrt{784}}{3} \) is equivalent to \( \frac{28}{3} \) since \( \sqrt{784} = 28 \).
So, to clarify:
- \( 9 \frac{1}{3} \) simplifies to \( \frac{28}{3} \).
- \( \frac{28}{3} = \frac{\sqrt{784}}{3} \).
Thank you for your patience!
\( 9 \frac{1}{3} = \frac{28}{3} \).
The expression \( \frac{\sqrt{784}}{3} \) is equivalent to \( \frac{28}{3} \) since \( \sqrt{784} = 28 \).
So, to clarify:
- \( 9 \frac{1}{3} \) simplifies to \( \frac{28}{3} \).
- \( \frac{28}{3} = \frac{\sqrt{784}}{3} \).
Thank you for your patience!
Answered by
GPT-4o mini
Yes, that's correct!
The mixed number \( 9 \frac{1}{3} \) is equal to \( \frac{28}{3} \).
The mixed number \( 9 \frac{1}{3} \) is equal to \( \frac{28}{3} \).
Answered by
GPT-4o mini
I apologize for any confusion earlier. Let's clarify the conversion from the mixed number \( 9 \frac{1}{3} \) properly.
To convert \( 9 \frac{1}{3} \) to an improper fraction:
1. Multiply the whole number (9) by the denominator (3):
\( 9 \times 3 = 27 \)
2. Add the numerator (1) to this result:
\( 27 + 1 = 28 \)
3. Place that total over the original denominator (3):
\( \frac{28}{3} \)
Thus, \( 9 \frac{1}{3} \) does indeed equal \( \frac{28}{3} \).
If you are tasked with rewriting \( 9 \frac{1}{3} \) in terms of a root, one possible presentation could be \( \frac{\sqrt{784}}{3} \) since \( \sqrt{784} = 28\).
If you received feedback stating this was incorrect, please verify the specific instruction or context for converting or rewriting. However, in mathematical terms, \( 9 \frac{1}{3} = \frac{28}{3} \) is accurate.
To convert \( 9 \frac{1}{3} \) to an improper fraction:
1. Multiply the whole number (9) by the denominator (3):
\( 9 \times 3 = 27 \)
2. Add the numerator (1) to this result:
\( 27 + 1 = 28 \)
3. Place that total over the original denominator (3):
\( \frac{28}{3} \)
Thus, \( 9 \frac{1}{3} \) does indeed equal \( \frac{28}{3} \).
If you are tasked with rewriting \( 9 \frac{1}{3} \) in terms of a root, one possible presentation could be \( \frac{\sqrt{784}}{3} \) since \( \sqrt{784} = 28\).
If you received feedback stating this was incorrect, please verify the specific instruction or context for converting or rewriting. However, in mathematical terms, \( 9 \frac{1}{3} = \frac{28}{3} \) is accurate.
Answered by
GPT-4o mini
Let me clarify:
The mixed number \( 9 \frac{1}{3} \) is indeed equal to \( \frac{28}{3} \), not \( \frac{27}{3} \).
Here's the breakdown:
1. The whole number part is 9.
2. The fractional part is \( \frac{1}{3} \).
To convert \( 9 \frac{1}{3} \) to an improper fraction:
1. Multiply the whole number (9) by the denominator (3):
\( 9 \times 3 = 27 \)
2. Add the numerator (1) to this result:
\( 27 + 1 = 28 \)
So, you get:
\[
9 \frac{1}{3} = \frac{28}{3}
\]
**Therefore, the correct value is \( \frac{28}{3} \).**
If it said something different, please make sure to recheck the instruction or context. If you meant just \( 9 \) (without the fraction), then \( 9 = \frac{27}{3} \), but with the fraction, it is definitely \( \frac{28}{3} \).
The mixed number \( 9 \frac{1}{3} \) is indeed equal to \( \frac{28}{3} \), not \( \frac{27}{3} \).
Here's the breakdown:
1. The whole number part is 9.
2. The fractional part is \( \frac{1}{3} \).
To convert \( 9 \frac{1}{3} \) to an improper fraction:
1. Multiply the whole number (9) by the denominator (3):
\( 9 \times 3 = 27 \)
2. Add the numerator (1) to this result:
\( 27 + 1 = 28 \)
So, you get:
\[
9 \frac{1}{3} = \frac{28}{3}
\]
**Therefore, the correct value is \( \frac{28}{3} \).**
If it said something different, please make sure to recheck the instruction or context. If you meant just \( 9 \) (without the fraction), then \( 9 = \frac{27}{3} \), but with the fraction, it is definitely \( \frac{28}{3} \).
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