freeCodeCamp/guide/english/mathematics/algebra/intro-to-rationalizing-the-denominator/index.md

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title: Intro to Rationalizing the Denominator
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## Intro to Rationalizing the Denominator

If a number couldn't be expressed in p/q form where p,q are real numbers and q in non-zero, the number is said to be an irrational number .To simplify the fraction we should rationalize the denominator. Rationalizing the denominator can aid you to simplify certain equations. This could be done by the following listed methods -

### Multiplying by a Root
We can multiply the top and bottom by a root. Notice that we are multiplying the fraction by root 2 divided by itself which is just another way or writing 1.  
 
<img src="https://github.com/codersc/freeCodeCamp-article-images/blob/master/art4img1.png?raw=true">

### Multiplying by a Conjugate
We can also multiply the top and bottom by the conjugate.
 
<img src="https://github.com/codersc/freeCodeCamp-article-images/blob/master/art4img2.png?raw=true">
 
<img src="https://github.com/codersc/freeCodeCamp-article-images/blob/master/art4img3.png?raw=true">