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Simplify the following expression by multiplying by the conjugate.

 

 Apr 25, 2020
 #1
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The conjugate of  [ sqrt(3) -1 ]  is  [ sqrt(3) + 1 ]

 

Numerator:  [ 6 + 10sqrt(3) ] · [ sqrt(3) + 1 ]  =  6sqrt(3) + 6 + 10sqrt(3)sqrt(3) + 10sqrt(3)

                                                                      =  6sqrt(3) + 6 + 10·3 + 10sqrt(3)

                                                                      =  16sqrt(3) + 36

 

Denominator:  [ sqrt(3) - 1 ] · [ sqrt(3) + 1 ]  =  3 - 1  =  2

 

Answer  =  [ 16sqrt(3) + 36 ] / 2  =  8sqrt(3) + 18

 Apr 25, 2020

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