Help with how to do this equation

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Discussion Overview

The discussion revolves around a mathematical equation involving rationalizing the denominator. Participants are exploring the steps involved in simplifying the expression and addressing uncertainties about the results obtained after applying the rationalization technique.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant suggests rationalizing the denominator by multiplying by \(\sqrt{3}\).
  • Another participant expresses uncertainty about the next steps after rationalization.
  • A participant questions the nature of the numbers \(a\) and \(b\), suggesting that if they are real numbers, there could be infinitely many correct answers, while specifying rational numbers would lead to a unique solution.
  • There is a request for clarification on the results obtained after rationalizing the denominator.

Areas of Agreement / Disagreement

Participants express uncertainty about the simplification process and the nature of the solutions, indicating a lack of consensus on the next steps and the implications of the problem's conditions.

Contextual Notes

There are unresolved questions regarding the assumptions about the types of numbers involved (real vs. rational) and the specific results obtained from the rationalization process.

ajk426
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Hint: Rationalize the denominator: [math]\dfrac{8 - \sqrt{27}}{2 \sqrt{3}} = \dfrac{8 - \sqrt{27}}{2 \sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}}[/math]

-Dan
 
I've done that but I'm not sure where to go from there.
 
ajk426 said:
I've done that but I'm not sure where to go from there.
You should have gotten a form that looks like [math]a + b \sqrt{3}[/math] so I don't know where the problem is. Please post what you got.

-Dan
 
When you multiplied both numerator and denominator by $\sqrt{3}$, what did you get?
 
Did the problem really say that a and b are real numbers? If so there are infinitely many correct answers. IF the problem had specified "rational number" then there would be a unique answer.
 

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