SOLUTION: Rationalize the Denominator for this:
4-sqrt(3)/6+sqrt(y)
I don't even know how to begin this. Could you help?
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Question 210004This question is from textbook Intro Alegbra
: Rationalize the Denominator for this:
4-sqrt(3)/6+sqrt(y)
I don't even know how to begin this. Could you help?
This question is from textbook Intro Alegbra
Found 3 solutions by stanbon, rapaljer, Alan3354:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Rationalize the Denominator for this:
4-sqrt(3)/6+sqrt(y)
------------------
Multiply numerator and denominator by (6-sqrt(y)) to get:
----
[(4-sqrt(3)(6-sqrt(y)]/[(6+sqrt(y))(6-sqrt(y)}
---
= [24 -4sqrt(y)-6sqrt(3)+sqrt(3y)]/[36-y]
============================================
Cheers,
Stan H.
Reply to stanbon@comcast.net
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Rationalizing the denominator means to get rid of all the square roots in the denominator. You can do this by multiplying the numerator and denominator by the same quantity, and in the case of binomial denominators, you must multiply by the same binomial as the denominator EXCEPT with the OPPOSITE SIGN. You may ask, why do we do this??? Because it works!! This will probably get ugly, so hang in there! I have a pretty good lesson for this (if I do say so myself!!)on my website! To see it, click on my tutor name "Rapaljer" anywhere in algebra.com, and look for the link on my homepage that says "MATH IN LIVING COLOR." Select "Intermediate Algebra" and look for "Chapter 3" which is on Square Roots and Radicals. Choose the topic that says "Rationalizing Denominators." Now back to the problem at hand.
You will have to multiply the numerator and denominator by
It looks like this:
*
This simplifies (but not much, but at least you eliminated the square roots from the denominator!)
R^2
Dr. Robert J. Rapalje
Seminole Community College
Altamonte Springs Campus
Florida
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Rationalize the Denominator for this:
4-sqrt(3)/6+sqrt(y)
----------
You ALWAYS multiply NUM and DEN by the conjugate of the DEN.
The conjugate is 6 - sqrt(y)
=
=
=
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