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Bentuk sederhana dari 23​+32​32​​ adalah ...

Pertanyaan

Bentuk sederhana dari fraction numerator 3 square root of 2 over denominator 2 square root of 3 plus 3 square root of 2 end fraction adalah ...space 

  1. 2 open parentheses 2 minus square root of 6 close parentheses 

  2. 4 minus square root of 6 

  3. 3 minus 2 square root of 6 

  4. 3 minus square root of 6 

  5. 2 minus square root of 6 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Diketahui fraction numerator 3 square root of 2 over denominator 2 square root of 3 plus 3 square root of 2 end fraction, maka kalikan pecahan tersebut dengan bentuk sekawan dari penyebutnya.

Bentuk sekawan dari 2 square root of 3 plus 3 square root of 2 adalah 2 square root of 3 minus 3 square root of 2.

Maka bentuk sederhana dari fraction numerator 3 square root of 2 over denominator 2 square root of 3 plus 3 square root of 2 end fraction adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 square root of 2 over denominator 2 square root of 3 plus 3 square root of 2 end fraction end cell equals cell fraction numerator 3 square root of 2 over denominator 2 square root of 3 plus 3 square root of 2 end fraction times fraction numerator 2 square root of 3 minus 3 square root of 2 over denominator 2 square root of 3 minus 3 square root of 2 end fraction end cell row blank equals cell fraction numerator 3 square root of 2 open parentheses 2 square root of 3 minus 3 square root of 2 close parentheses over denominator open parentheses 2 square root of 3 close parentheses squared minus open parentheses 3 square root of 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator 3 square root of 2 open parentheses 2 square root of 3 minus 3 square root of 2 close parentheses over denominator 12 minus 18 end fraction end cell row blank equals cell fraction numerator 3 square root of 2 open parentheses 2 square root of 3 minus 3 square root of 2 close parentheses over denominator negative 6 end fraction end cell row blank equals cell fraction numerator square root of 2 open parentheses 2 square root of 3 minus 3 square root of 2 close parentheses over denominator negative 2 end fraction end cell row blank equals cell fraction numerator square root of 2 times 2 square root of 3 minus square root of 2 times 3 square root of 2 over denominator negative 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus 6 over denominator negative 2 end fraction space open parentheses sama minus sama space dibagi space minus 2 close parentheses end cell row blank equals cell negative square root of 6 plus 3 end cell row blank equals cell 3 minus square root of 6 end cell end table 

Jadi, jawaban yang tepat adalah D.

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