MHB Why is the book's answer for rationalizing the denominator x^(3/2)?

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The discussion centers on the rationalization of the denominator in the expression $\dfrac{4}{\sqrt{x^3}}$. The correct answer, as per the book, is $x^{3/2}$, which can be derived by rewriting the expression as $\dfrac{4}{x\sqrt{x}} \cdot \dfrac{\sqrt{x}}{\sqrt{x}} = \dfrac{4\sqrt{x}}{x^2}$. Participants emphasize that arriving at a different answer does not invalidate the process, highlighting the importance of understanding the reasoning behind the solution rather than just the final result.

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mathdad
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Rationalize the denominator. See picture for my answer. The book's answer is x^(3/2). Why?

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note $x >0$ ...

$\dfrac{4}{\sqrt{x^3}} = \dfrac{4}{x\sqrt{x}} \cdot \dfrac{\sqrt{x}}{\sqrt{x}}= \dfrac{4\sqrt{x}}{x^2}$
 
I got the same answer you did after several tries. It is very discouraging and depressing because I really love math. I can't even get the simple questions right.
 
RTCNTC said:
I got the same answer you did after several tries. It is very discouraging and depressing because I really love math. I can't even get the simple questions right.

It is this very process, that in time, will make you love math even more! The point is not that you arrived at an incorrect answer, but rather why you didn't arrive at the correct one. Keep at it!
 
I will continue to press forward with hearts courageous.
 
RTCNTC said:
I got the same answer you did after several tries. It is very discouraging and depressing because I really love math. I can't even get the simple questions right.

Your answer is fine. It may not be what the book says, but that doesn't make it wrong - just a different form. Is it technically "lowest terms"? Maybe not. I wouldn't worry about it too much.
 
Thank you everyone.
 

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