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

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Discussion Overview

The discussion revolves around the process of rationalizing the denominator in a mathematical expression, specifically addressing a discrepancy between a participant's answer and the answer provided in a book. The scope includes mathematical reasoning and exploration of different forms of answers.

Discussion Character

  • Exploratory, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents their rationalization process and questions why the book's answer is x^(3/2).
  • Another participant provides a step-by-step breakdown of their rationalization, showing the transformation of the expression.
  • Several participants express feelings of discouragement over not arriving at the book's answer, indicating a struggle with the material.
  • One participant reassures others that differing answers may not be incorrect but rather different forms, questioning the notion of "lowest terms."
  • Encouragement is offered to continue engaging with the material despite challenges.

Areas of Agreement / Disagreement

Participants generally express disagreement regarding the correctness of their answers compared to the book's answer, with multiple views on what constitutes an acceptable form of the answer. The discussion remains unresolved as to whether the book's answer is definitive.

Contextual Notes

Some participants note the importance of understanding the reasoning behind their answers rather than solely focusing on arriving at the correct answer. There is an acknowledgment of the emotional challenges faced when grappling with mathematical concepts.

Who May Find This Useful

Individuals interested in mathematical problem-solving, particularly those struggling with rationalizing denominators or seeking reassurance in their mathematical journey.

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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Mathematics news on Phys.org
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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