Question
Perform the indicated operation be sure to rationalize the denominator when necessary make sure to simply as much as possible and give the exact answer
8 divided by square root of 3
8 divided by square root of 3
Answers
GPT-4o mini
To divide 8 by the square root of 3, we start with the expression:
\[
\frac{8}{\sqrt{3}}
\]
To rationalize the denominator, we multiply the numerator and denominator by \(\sqrt{3}\):
\[
\frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{3}
\]
So, the simplified expression is:
\[
\frac{8\sqrt{3}}{3}
\]
This is the exact answer.
\[
\frac{8}{\sqrt{3}}
\]
To rationalize the denominator, we multiply the numerator and denominator by \(\sqrt{3}\):
\[
\frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{3}
\]
So, the simplified expression is:
\[
\frac{8\sqrt{3}}{3}
\]
This is the exact answer.
K
That is not correct
GPT-4o mini
I apologize for any confusion. Let's go through the calculation again step by step.
We start with the expression:
\[
\frac{8}{\sqrt{3}}
\]
To rationalize the denominator, we multiply both the numerator and the denominator by \(\sqrt{3}\):
\[
\frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{3}
\]
This form \(\frac{8\sqrt{3}}{3}\) is indeed the rationalized form of \(\frac{8}{\sqrt{3}}\), and it is simplified as much as possible.
So, the correct final answer remains:
\[
\frac{8\sqrt{3}}{3}
\]
If there is something specific you believe is incorrect, please clarify, and I'd be glad to assist further!
We start with the expression:
\[
\frac{8}{\sqrt{3}}
\]
To rationalize the denominator, we multiply both the numerator and the denominator by \(\sqrt{3}\):
\[
\frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{3}
\]
This form \(\frac{8\sqrt{3}}{3}\) is indeed the rationalized form of \(\frac{8}{\sqrt{3}}\), and it is simplified as much as possible.
So, the correct final answer remains:
\[
\frac{8\sqrt{3}}{3}
\]
If there is something specific you believe is incorrect, please clarify, and I'd be glad to assist further!
K
You repeated the same thing
GPT-4o mini
I apologize for any misunderstanding or frustration. Let’s confirm the steps clearly and see if there's anything I might have missed or miscommunicated:
1. **Original expression:**
\[
\frac{8}{\sqrt{3}}
\]
2. **Rationalize the denominator:** Multiply both the numerator and the denominator by \(\sqrt{3}\):
\[
\frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{3}
\]
3. **Result:**
\[
\frac{8\sqrt{3}}{3}
\]
This indeed is the fully simplified and rationalized form of \(\frac{8}{\sqrt{3}}\).
If there's a different aspect of the problem you'd like to address or if a different calculation was intended, please let me know, and I’ll do my best to assist you accordingly! Thank you for your patience.
1. **Original expression:**
\[
\frac{8}{\sqrt{3}}
\]
2. **Rationalize the denominator:** Multiply both the numerator and the denominator by \(\sqrt{3}\):
\[
\frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{3}
\]
3. **Result:**
\[
\frac{8\sqrt{3}}{3}
\]
This indeed is the fully simplified and rationalized form of \(\frac{8}{\sqrt{3}}\).
If there's a different aspect of the problem you'd like to address or if a different calculation was intended, please let me know, and I’ll do my best to assist you accordingly! Thank you for your patience.
K
How do you write that
GPT-4o mini
Sure! Here's the rationalization process and final answer clearly written out:
### Problem
Divide \( 8 \) by \( \sqrt{3} \) and rationalize the denominator.
### Solution
1. **Start with the expression:**
\[
\frac{8}{\sqrt{3}}
\]
2. **Rationalize the denominator:** Multiply the numerator and denominator by \( \sqrt{3} \):
\[
\frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{3}
\]
### Final Answer
The exact answer, with the denominator rationalized, is:
\[
\frac{8\sqrt{3}}{3}
\]
Let me know if there's anything else you need!
### Problem
Divide \( 8 \) by \( \sqrt{3} \) and rationalize the denominator.
### Solution
1. **Start with the expression:**
\[
\frac{8}{\sqrt{3}}
\]
2. **Rationalize the denominator:** Multiply the numerator and denominator by \( \sqrt{3} \):
\[
\frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{3}
\]
### Final Answer
The exact answer, with the denominator rationalized, is:
\[
\frac{8\sqrt{3}}{3}
\]
Let me know if there's anything else you need!