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

Question

8 divided by square root of 3

Answer 1

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.

Answer 2

That is not correct

Answer 3

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!

Answer 4

You repeated the same thing

Answer 5

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.

Answer 6

How do you write that

Answer 7

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!