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Bentuk sederhana dari  adalah

Pertanyaan

Bentuk sederhana dari fraction numerator 8 over denominator square root of 13 minus 3 end fraction adalah horizontal ellipsis 

  1. 5 square root of 13 plus 3 

  2. 2 square root of 13 plus 6 

  3. 2 square root of 13 minus 6 

  4. 5 square root of 13 minus 3 

Pembahasan Video:

Pembahasan Soal:

Ingat kembali cara merasionalkan bentuk akar dengan mengalikan akar sekawan berikut:

fraction numerator 1 over denominator square root of b minus a end fraction equals fraction numerator 1 over denominator square root of b minus a end fraction cross times fraction numerator square root of b plus a over denominator square root of b plus a end fraction

Dengan menggunakan sifat di atas, maka bentuk sederhana dari fraction numerator 8 over denominator square root of 13 minus 3 end fraction adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 8 over denominator square root of 13 minus 3 end fraction end cell equals cell fraction numerator 8 over denominator square root of 13 minus 3 end fraction cross times fraction numerator square root of 13 plus 3 over denominator square root of 13 plus 3 end fraction end cell row blank equals cell fraction numerator 8 open parentheses square root of 13 plus 3 close parentheses over denominator 13 plus up diagonal strike 3 square root of 13 end strike minus up diagonal strike 3 square root of 13 end strike minus 9 end fraction end cell row blank equals cell fraction numerator up diagonal strike 8 open parentheses square root of 13 plus 3 close parentheses over denominator up diagonal strike 4 end fraction end cell row blank equals cell 2 open parentheses square root of 13 plus 3 close parentheses end cell row cell fraction numerator 8 over denominator square root of 13 minus 3 end fraction end cell equals cell 2 square root of 13 plus 6 end cell end table

Jadi, bentuk sederhana dari fraction numerator 8 over denominator square root of 13 minus 3 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 13 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table 

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 13 September 2021

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Pertanyaan yang serupa

Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Hasilnya didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 10 over denominator 4 minus square root of 11 end fraction end cell equals cell fraction numerator 10 over denominator 4 minus square root of 11 end fraction cross times fraction numerator 4 plus square root of 11 over denominator 4 plus square root of 11 end fraction end cell row blank equals cell fraction numerator 10 open parentheses 4 plus square root of 11 close parentheses over denominator 16 minus 11 end fraction end cell row blank equals cell fraction numerator 10 open parentheses 4 plus square root of 11 close parentheses over denominator 5 end fraction end cell row blank equals cell 2 open parentheses 4 plus square root of 11 close parentheses end cell row blank equals cell 8 plus 2 square root of 11 end cell end table 

Dengan demikian, bentuk sederhana dari fraction numerator 10 over denominator 4 minus square root of 11 end fraction adalah 8 plus 2 square root of 11.

Jadi, jawaban yang benar adalah A.

0

Roboguru

Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Ingat kembali:

open parentheses straight a minus square root of straight b close parentheses open parentheses straight a plus square root of straight b close parentheses equals straight a squared minus open parentheses square root of straight b close parentheses squared 

Bentuk sederhana dari fraction numerator 6 over denominator 3 minus square root of 7 end fraction dapat ditentukan dengan cara:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 over denominator 3 minus square root of 7 end fraction end cell equals cell fraction numerator 6 over denominator 3 minus square root of 7 end fraction cross times fraction numerator 3 plus square root of 7 over denominator 3 plus square root of 7 end fraction end cell row blank equals cell fraction numerator 6 open parentheses 3 plus square root of 7 close parentheses over denominator 3 squared minus open parentheses square root of 7 close parentheses squared end fraction end cell row blank equals cell fraction numerator 6 open parentheses 3 plus square root of 7 close parentheses over denominator 9 minus 7 end fraction end cell row blank equals cell fraction numerator 6 open parentheses 3 plus square root of 7 close parentheses over denominator 2 end fraction end cell row blank equals cell 3 open parentheses 3 plus square root of 7 close parentheses end cell row blank equals cell 9 plus 3 square root of 7 end cell end table 

Jadi, jawaban yang benar adalah A.

0

Roboguru

Bentuk sederhana dari  = ...

Pembahasan Soal:

Penyederhanaan bentuk akar dapat dilakukan dengan mengalikan bentuk akar tersebut dengan akar sekawan

begin mathsize 12px style fraction numerator a over denominator b square root of b minus square root of c end fraction  equals fraction numerator a over denominator b square root of b minus square root of c end fraction cross times fraction numerator open parentheses b square root of b plus square root of c close parentheses over denominator open parentheses b square root of b plus square root of c close parentheses end fraction  equals fraction numerator a open parentheses b square root of b plus square root of c close parentheses over denominator b cubed minus c end fraction    fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction  equals fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction cross times fraction numerator open parentheses 2 square root of 2 plus square root of 5 close parentheses over denominator open parentheses 2 square root of 2 plus square root of 5 close parentheses end fraction  equals fraction numerator 18 square root of 2 plus 9 square root of 5 over denominator 4 cross times 2 minus 5 end fraction  equals fraction numerator 18 square root of 2 plus 9 square root of 5 over denominator 8 minus 5 end fraction  equals fraction numerator 18 square root of 2 plus 9 square root of 5 over denominator 3 end fraction  equals 6 square root of 2 plus 3 square root of 5 end style

Jadi, begin mathsize 12px style fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction equals 6 square root of 2 plus 3 square root of 5 end style

0

Roboguru

Rasionalkan setiap bentuk akar berikut. d).

Pembahasan Soal:

Ingat:

begin mathsize 14px style fraction numerator 1 over denominator square root of a minus square root of b end fraction equals fraction numerator 1 over denominator square root of a minus square root of b end fraction cross times fraction numerator square root of a plus square root of b over denominator square root of a plus square root of b end fraction equals fraction numerator square root of a plus square root of b over denominator a minus b end fraction end style

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 over denominator square root of 5 minus square root of 3 end fraction end cell equals cell fraction numerator 6 over denominator square root of 5 minus square root of 3 end fraction cross times fraction numerator square root of 5 plus square root of 3 over denominator square root of 5 plus square root of 3 end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 5 plus square root of 3 close parentheses over denominator open parentheses square root of 5 minus square root of 3 close parentheses open parentheses square root of 5 plus square root of 3 close parentheses end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 5 plus square root of 3 close parentheses over denominator 5 minus 3 end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 5 plus square root of 3 close parentheses over denominator 2 end fraction end cell row blank equals cell 3 open parentheses square root of 5 plus square root of 3 close parentheses end cell end table end style

Jadi, jawaban yang tepat adalah begin mathsize 14px style 3 open parentheses square root of 5 plus square root of 3 close parentheses end style.

3

Roboguru

Bentuk rasional dari  adalah ....

Pembahasan Soal:

Penyebut pecahan berbentuk akar dapat dirasionalkan dengan sifat perkalian bentuk sekawan seperti berikut,

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 over denominator square root of 3 plus 1 end fraction end cell equals cell fraction numerator 6 over denominator square root of 3 plus 1 end fraction times fraction numerator square root of 3 minus 1 over denominator square root of 3 minus 1 end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 3 minus 1 close parentheses over denominator 3 minus 1 end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 3 minus 1 close parentheses over denominator 2 end fraction end cell row blank equals cell 3 open parentheses square root of 3 minus 1 close parentheses end cell end table  

Dengan demikian, bentuk rasionalnya adalah 3 open parentheses square root of 3 minus 1 close parentheses.

Jadi, jawaban yang tepat adalah A.

0

Roboguru

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