MHB Help with how to do this equation

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The discussion focuses on rationalizing the denominator of the expression \(\frac{8 - \sqrt{27}}{2 \sqrt{3}}\) by multiplying both the numerator and denominator by \(\sqrt{3}\). Participants emphasize the importance of achieving a form that resembles \(a + b \sqrt{3}\). The conversation highlights that if the problem specifies that \(a\) and \(b\) are real numbers, multiple correct answers exist, while a specification of "rational numbers" would yield a unique solution.

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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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