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Rationalizing


A fraction is not considered simplified until all the radicals have been removed from the denominator. If a denominator contains a single term with a square root, it can be rationalized by multiplying both the numerator and denominator by that square root. If the denominator contains square roots separated by a plus or minus sign, then multiply both the numerator and denominator by the conjugate, which is formed by merely changing the sign between the roots.

 

Example 1: Rationalize the fraction 235
 

Multiply top and bottom of the fraction by √5

235·55 = 253·25 = 253·5 = 2515

 

Example 2: Rationalize the fraction 23-5

Multiply top and bottom of the fraction by the conjugate (3+√5):

23-5·3+53+5 = 23+532+35-35-52

= 23+59-5 = 23+54

= 3+52




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