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Rasionalkan bentuk berikut. a. 32​−14​82​​

Pertanyaan

Rasionalkan bentuk berikut.

a. fraction numerator 8 square root of 2 over denominator 3 square root of 2 minus square root of 14 end fraction

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

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Jawaban

bentuk rasional dari fraction numerator 8 square root of 2 over denominator 3 square root of 2 minus square root of 14 end fraction adalah 4 open parentheses 3 plus square root of 7 close parentheses.

Pembahasan

Ingat bahwa:

  • Merasionalkan pecahan bentuk fraction numerator a over denominator square root of b plus square root of c end fraction dapat dengan mengalikan pecahan bentuk akar tersebut dengan akar sekawannya yaitu fraction numerator square root of b plus square root of c over denominator square root of b plus square root of c end fraction.
  • square root of a b end root equals square root of a square root of b square root of a square root of a equals a open parentheses a b close parentheses to the power of c equals a to the power of c b to the power of c open parentheses square root of a close parentheses squared equals a a open parentheses b plus c close parentheses equals a b plus a c open parentheses a minus b close parentheses open parentheses a plus b close parentheses equals a squared minus b squared 

Merasionalkan bentuk fraction numerator 8 square root of 2 over denominator 3 square root of 2 minus square root of 14 end fraction:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 8 square root of 2 over denominator 3 square root of 2 minus square root of 14 end fraction end cell equals cell fraction numerator 8 square root of 2 over denominator 3 square root of 2 minus square root of 14 end fraction end cell row blank equals cell fraction numerator 8 square root of 2 open parentheses 3 square root of 2 plus square root of 14 close parentheses over denominator open parentheses 3 square root of 2 minus square root of 14 close parentheses open parentheses 3 square root of 2 plus square root of 14 close parentheses end fraction end cell row blank equals cell fraction numerator 8 square root of 2 times thin space 3 square root of 2 plus 8 square root of 2 square root of 14 over denominator open parentheses 3 square root of 2 close parentheses squared minus open parentheses square root of 14 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 cubed times thin space 3 square root of 2 square root of 2 plus 2 cubed square root of 2 square root of 2 times thin space 7 end root over denominator 3 squared open parentheses square root of 2 close parentheses squared minus 14 end fraction end cell row blank equals cell fraction numerator 2 cubed times thin space 3 times thin space 2 plus 2 cubed square root of 2 square root of 2 square root of 7 over denominator 9 times thin space 2 minus 14 end fraction end cell row blank equals cell fraction numerator 2 cubed times thin space 3 times thin space 2 plus 2 cubed times thin space 2 square root of 7 over denominator 18 minus 14 end fraction end cell row blank equals cell fraction numerator 48 plus 16 square root of 7 over denominator 4 end fraction end cell row blank equals cell fraction numerator 16 open parentheses 3 plus square root of 7 close parentheses over denominator 4 end fraction end cell row blank equals cell 4 open parentheses 3 plus square root of 7 close parentheses end cell end table 

Jadi, bentuk rasional dari fraction numerator 8 square root of 2 over denominator 3 square root of 2 minus square root of 14 end fraction adalah 4 open parentheses 3 plus square root of 7 close parentheses.

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