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Bentuk sederhana dari  adalah ....

Bentuk sederhana dari begin mathsize 14px style fraction numerator 2 square root of 6 over denominator square root of 3 plus square root of 2 end fraction end style adalah ....

  1. begin mathsize 14px style 2 open parentheses 3 square root of 2 minus 2 square root of 3 close parentheses end style 

  2. begin mathsize 14px style 2 open parentheses 3 square root of 2 plus 2 square root of 3 close parentheses end style 

  3. begin mathsize 14px style 2 open parentheses 2 square root of 2 plus 3 square root of 3 close parentheses end style 

  4. begin mathsize 14px style 2 open parentheses 2 square root of 2 minus 3 square root of 3 close parentheses end style 

  5. begin mathsize 14px style 3 open parentheses 3 square root of 2 plus 2 square root of 3 close parentheses end style 

Jawaban:

Bentuk akar dalam pecahan dapat disederhanakan dengan mengalikan sekawan.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 6 over denominator square root of 3 plus square root of 2 end fraction times fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 minus square root of 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 times open parentheses square root of 3 minus square root of 2 close parentheses over denominator open parentheses square root of 3 plus square root of 2 close parentheses open parentheses square root of 3 minus square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator 2 open parentheses square root of 18 minus square root of 12 close parentheses over denominator 3 minus 2 end fraction end cell row blank equals cell 2 open parentheses 3 square root of 2 minus 2 square root of 3 close parentheses end cell end table end style 

Dengan demikian bentuk sederhana dari begin mathsize 14px style fraction numerator 2 square root of 6 over denominator square root of 3 plus square root of 2 end fraction end style adalah begin mathsize 14px style 2 open parentheses 3 square root of 2 minus 2 square root of 3 close parentheses end style.

Jadi, jawaban yang tepat adalah A.

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