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

  • MHB
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In summary, rationalizing the denominator involves manipulating the fraction to remove any radicals from the denominator. In the conversation, the participants discuss the steps for rationalizing the denominator and arrive at different answers. Despite initial frustration, the importance of perseverance and understanding the process is emphasized.
  • #1
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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  • #2
note $x >0$ ...

$\dfrac{4}{\sqrt{x^3}} = \dfrac{4}{x\sqrt{x}} \cdot \dfrac{\sqrt{x}}{\sqrt{x}}= \dfrac{4\sqrt{x}}{x^2}$
 
  • #3
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.
 
  • #4
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!
 
  • #5
I will continue to press forward with hearts courageous.
 
  • #6
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.
 
  • #7
Thank you everyone.
 

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

1. What does it mean to "rationalize the denominator"?

Rationalizing the denominator refers to the process of simplifying a fraction by removing any square roots, cube roots, or other radical expressions from the denominator. This is done by multiplying both the numerator and denominator by an appropriate factor.

2. Why is it important to rationalize the denominator?

Rationalizing the denominator is important because it allows for easier computation and comparison of fractions. It also helps to eliminate any complex or irrational numbers in the denominator, making the fraction more simplified.

3. How do you rationalize a denominator with a single radical?

To rationalize a denominator with a single radical, multiply the numerator and denominator by the conjugate of the radical. The conjugate is the same expression as the radical, but with the opposite sign in the middle. This will result in a simplified fraction with no radical in the denominator.

4. Can you rationalize a denominator with multiple radicals?

Yes, you can rationalize a denominator with multiple radicals by following the same process as with a single radical. Multiply the numerator and denominator by the conjugate of each radical, and then simplify the resulting fraction.

5. Are there any situations where rationalizing the denominator is not necessary?

Yes, there are some situations where rationalizing the denominator may not be necessary. For example, in some cases, a fraction with a radical in the denominator may already be simplified and cannot be further simplified by rationalizing. Additionally, some mathematical equations may require a radical in the denominator for the solution to be correct.

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