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Rasionalkan penyebut pecahan berikut .

Rasionalkan penyebut pecahan berikut begin mathsize 14px style fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction end style.

  1. begin mathsize 14px style 4 square root of 3 end style 

  2. size 14px 2 size 14px plus size 14px 4 square root of size 14px 3 

  3. size 14px 5 size 14px plus size 14px 4 square root of size 14px 3 

  4. size 14px 7 size 14px plus size 14px 4 square root of size 14px 3 

  5. begin mathsize 14px style square root of 3 end style 

Jawaban:

Bilangan ini dapat dirasionalkan dengan perkalian sekawan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction cross times fraction numerator 2 plus square root of 3 over denominator 2 plus square root of 3 end fraction end cell equals cell fraction numerator open parentheses 2 plus square root of 3 close parentheses left parenthesis 2 plus square root of 3 right parenthesis over denominator left parenthesis 2 minus square root of 3 right parenthesis left parenthesis 2 plus square root of 3 right parenthesis end fraction end cell row blank equals cell fraction numerator 4 plus 2 square root of 3 plus 2 square root of 3 plus 3 over denominator 4 minus 3 end fraction end cell row blank equals cell 7 plus 4 square root of 3 end cell end table end style

Jadi, jawaban yang tepat adalah D.

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