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Pertanyaan

fraction numerator 2 over denominator 1 plus square root of 3 end fraction equals 

Pembahasan Video:

Pembahasan Soal:

Diasumsikan soal tersebut adalah mencari bentuk rasional.

Untuk mencari bentuk rasional dari pecahan bentuk fraction numerator straight a over denominator straight b plus square root of straight c end fraction adalah dengan mengalikannya dengan fraction numerator straight b minus square root of straight c over denominator straight b minus square root of straight c end fraction 

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 over denominator 1 plus square root of 3 end fraction end cell equals cell fraction numerator 2 over denominator 1 plus square root of 3 end fraction cross times fraction numerator 1 minus square root of 3 over denominator 1 minus square root of 3 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 1 minus square root of 3 right parenthesis over denominator left parenthesis 1 plus square root of 3 right parenthesis left parenthesis 1 minus square root of 3 right parenthesis end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 1 minus square root of 3 right parenthesis over denominator 1 plus square root of 3 minus square root of 3 minus 3 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 1 minus square root of 3 right parenthesis over denominator 1 minus 3 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 1 minus square root of 3 right parenthesis over denominator negative 2 end fraction end cell row blank equals cell negative 1 left parenthesis 1 minus square root of 3 right parenthesis end cell row blank equals cell negative 1 plus square root of 3 end cell row blank equals cell square root of 3 minus 1 end cell end table   

Jadi, nilai dari fraction numerator 2 over denominator 1 plus square root of 3 end fraction adalah square root of 3 minus 1   

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 13 September 2021

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Pertanyaan yang serupa

Rasionalkan penyebut bentuk-bentuk akar berikut. a.

Pembahasan Soal:

Ingat kembali cara merasionalkan pecahan dengan penyebut bentuk akar.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator 2 minus square root of 2 over denominator square root of 2 end fraction end cell equals cell fraction numerator 2 minus square root of 2 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus square root of 2 cross times 2 end root over denominator square root of 2 cross times 2 end root end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus square root of 4 over denominator square root of 4 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus 2 over denominator 2 end fraction end cell row blank equals cell square root of 2 minus 1 end cell end table

Jadi, diperoleh fraction numerator 2 minus square root of 2 over denominator square root of 2 end fraction equals square root of 2 minus 1.

0

Roboguru

Hasil dari adalah ....

Pembahasan Soal:

Ingat : rightwards double arrow square root of a cross times square root of b equals square root of a cross times b end root rightwards double arrow a square root of b plus-or-minus c square root of b equals open parentheses a plus-or-minus c close parentheses square root of b

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 24 open parentheses square root of 8 minus 2 square root of 3 close parentheses plus fraction numerator 24 over denominator square root of 2 end fraction end cell equals cell square root of 192 minus 2 square root of 72 plus fraction numerator 24 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell square root of 64 cross times 3 end root minus 2 square root of 36 cross times 2 end root plus 24 over 2 square root of 2 end cell row blank equals cell 8 square root of 3 minus 12 square root of 2 plus 12 square root of 2 end cell row blank equals cell 8 square root of 3 end cell end table

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Rasionalkan penyebut pecahan-pecachan berikut!

Pembahasan Soal:

Ingat kembali aturan berikut. 

  • square root of a cross times square root of b equals square root of a cross times b end root 
  • Bentuk akar fraction numerator square root of a over denominator square root of b end fraction dapat dirasionalkan dengan cara fraction numerator square root of a over denominator square root of b end fraction cross times fraction numerator square root of b over denominator square root of b end fraction 
  • open parentheses a minus b close parentheses cross times square root of c equals a cross times square root of c minus b cross times square root of c 
  • p square root of a plus p square root of b equals p open parentheses square root of a plus square root of b close parentheses 

Dari rumus di atas, diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction end cell equals cell fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction cross times fraction numerator square root of 8 over denominator square root of 8 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 3 minus 4 close parentheses cross times square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 3 cross times square root of 8 minus 4 cross times square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 3 cross times 8 end root minus 4 square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 24 minus 4 square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 2 squared cross times 6 end root minus 4 square root of 2 squared cross times 2 end root over denominator 8 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus 4 cross times 2 square root of 2 over denominator 8 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus 8 square root of 2 over denominator 8 end fraction end cell row blank equals cell fraction numerator up diagonal strike 2 to the power of 1 cross times open parentheses square root of 6 minus 4 square root of 2 close parentheses over denominator up diagonal strike 8 to the power of 4 end fraction end cell row blank equals cell fraction numerator square root of 6 minus 4 square root of 2 over denominator 4 end fraction end cell end table 

Jadi, hasil dari merasionalkan fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 6 minus 4 square root of 2 over denominator 4 end fraction end cell end table.

0

Roboguru

Rasionalkan penyebut pecahan-pecahan berikut!

Pembahasan Soal:

Ingat kembali cara merasionalkan bentuk akar berikut!

  • fraction numerator 1 over denominator a plus square root of b end fraction equals fraction numerator 1 over denominator a plus square root of b end fraction cross times fraction numerator a minus square root of b over denominator a minus square root of b end fraction
  • table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis a plus square root of b right parenthesis left parenthesis a minus square root of b right parenthesis end cell equals cell a squared minus left parenthesis square root of b right parenthesis squared end cell end table  
  • c left parenthesis a minus square root of b right parenthesis equals c a minus c square root of b 

Dengan rumus di atas, diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 over denominator 3 plus square root of 2 end fraction end cell equals cell fraction numerator 3 over denominator 3 plus square root of 2 end fraction cross times fraction numerator 3 minus square root of 2 over denominator 3 minus square root of 2 end fraction end cell row blank equals cell fraction numerator 3 left parenthesis 3 minus square root of 2 right parenthesis over denominator left parenthesis 3 plus square root of 2 right parenthesis left parenthesis 3 minus square root of 2 right parenthesis end fraction end cell row blank equals cell fraction numerator 9 minus 3 square root of 2 over denominator 3 squared minus left parenthesis square root of 2 right parenthesis squared end fraction end cell row blank equals cell fraction numerator 9 minus 3 square root of 2 over denominator 9 minus 2 end fraction end cell row blank equals cell fraction numerator 9 minus 3 square root of 2 over denominator 7 end fraction end cell end table 

Jadi, bentuk rasional dari fraction numerator 3 over denominator 3 plus square root of 2 end fraction adalah fraction numerator 9 minus 3 square root of 2 over denominator 7 end fraction.

0

Roboguru

Bentuk rasional dari  adalah

Pembahasan Soal:

Merasionalkan bentuk akar dapat dilakukan dengan mengalikan penyebut akar dengan akar sekawannya. Diketahui fraction numerator 5 over denominator 5 plus square root of 3 end fraction maka akar sekawan dari penyebut 5 plus square root of 3 adalah 5 minus square root of 3 sehingga diperoleh

fraction numerator 5 over denominator 5 plus square root of 3 end fraction equals fraction numerator 5 over denominator 5 plus square root of 3 end fraction cross times fraction numerator 5 minus square root of 3 over denominator 5 minus square root of 3 end fraction

Berdasarkan sifat distributif perkalian yaitu open parentheses a plus b close parentheses open parentheses c plus d close parentheses equals a c plus a d plus b c plus b d dan a open parentheses b minus c close parentheses equals a b minus b cmaka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 over denominator 5 plus square root of 3 end fraction end cell equals cell fraction numerator 5 over denominator 5 plus square root of 3 end fraction cross times fraction numerator 5 minus square root of 3 over denominator 5 minus square root of 3 end fraction end cell row blank equals cell fraction numerator 5 open parentheses 5 minus square root of 3 close parentheses over denominator 5 cross times 5 minus 5 cross times square root of 3 plus 5 cross times square root of 3 minus square root of 3 cross times square root of 3 end fraction end cell row blank equals cell fraction numerator 5 cross times 5 minus 5 cross times square root of 3 over denominator 25 up diagonal strike negative 5 square root of 3 plus 5 square root of 3 end strike minus square root of 3 cross times square root of 3 end fraction end cell row blank equals cell fraction numerator 25 minus 5 square root of 3 over denominator 25 minus square root of 3 cross times square root of 3 end fraction end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root comma space a not equal to 0 space text dan end text space b not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 over denominator 5 plus square root of 3 end fraction end cell equals cell fraction numerator 25 minus 5 square root of 3 over denominator 25 minus square root of 3 cross times square root of 3 end fraction end cell row blank equals cell fraction numerator 25 minus 5 square root of 3 over denominator 25 minus square root of 3 cross times 3 end root end fraction end cell row blank equals cell fraction numerator 25 minus 5 square root of 3 over denominator 25 minus square root of 9 end fraction end cell row blank equals cell fraction numerator 25 minus 5 square root of 3 over denominator 25 minus 3 end fraction end cell row blank equals cell fraction numerator 25 minus 5 square root of 3 over denominator 22 end fraction end cell end table

Jadi bentuk rasional dari fraction numerator 5 over denominator 5 plus square root of 3 end fraction adalah fraction numerator 25 minus 5 square root of 3 over denominator 22 end fraction.

Oleh karena itu, jawaban yang tepat adalah A.

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