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Seriously stuck on rationalizing denominators.

by LaLea
(Charlotte,NC)











































They give the example of the square root (radical sign) 13/11 and they want it in it's simplest form and they don't explain very clearly how to do so. Please HELP!!!!

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May 23, 2011
Rationalizing the Denominator
by: Staff


The question:

by LaLea
(Charlotte, NC)

They give the example of the square root (radical sign) 13/11 and they want it in it's simplest form and they don't explain very clearly how to do so. Please HELP!!!!



The answer:

square root (radical sign) 13/11

= sqrt(13/11)

= sqrt(13)/sqrt(11)

Now we are going to eliminate the radical sign in the denominator. This is what is called rationalizing the denominator.

To accomplish this, multiply the current fraction [sqrt(13)/sqrt(11)] by another fraction [sqrt(11)/sqrt(11)].


There are two things to keep in mind:

1) The second fraction [sqrt(11)/sqrt(11)] is equal to 1.

sqrt(11)/sqrt(11) = 1

You are only multiplying the first fraction [sqrt(13)/sqrt(11)] by 1. This does not change the value of the first fraction. Anything multiplied by 1 is still the value you started with.

[sqrt(13)/sqrt(11)] * 1 = sqrt(13)/sqrt(11)


2) There is a point to the whole process. This is the point: remove the radical sign from the denominator of the first fraction.

The denominator of the first fraction and the denominator of the second fraction are both the same:

Denominator of the first fraction [sqrt(13)/sqrt(11)] is: sqrt(11)

Denominator of the second fraction [sqrt(11)/sqrt(11)] is also: sqrt(11)

Multiplying the sqrt(11) by sqrt(11) eliminates the square root sign. That is the only reason we are multiplying the two fractions.

sqrt(11) * sqrt(11) = 11


The complete process looks like this:

[sqrt(13)/sqrt(11)] * [sqrt(11)/sqrt(11)]

Multiply both numerators and multiply both denominators, just as you would when multiplying any two fractions:

= {[sqrt(13)] * [sqrt(11)]}/{[sqrt(11)] * [sqrt(11)]}

= {[sqrt(13)] * [sqrt(11)]}/11

You are finished with the process of rationalizing the denominator.


The final answer is: {[sqrt(13)] * [sqrt(11)]}/11


You may want to leave the expression as it is, or simplify the numerator:

{[sqrt(13)] * [sqrt(11)]}/11

= sqrt(13*11)/11

= sqrt(143)/11


The final answer could be written as:

{[sqrt(13)] * [sqrt(11)]}/11

or,

sqrt(143)/11


the real point is that there is no square root sign in the denominator




Thanks for writing.

Staff
www.solving-math-problems.com



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