Roboguru

Tentukan hasil dari bentuk akar berikut. a.

Pertanyaan

Tentukan hasil dari bentuk akar berikut.

a. begin mathsize 14px style open parentheses fourth root of 5 cubed end root close parentheses squared end style

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fourth root of 5 cubed end root close parentheses squared end cell equals cell open parentheses 5 to the power of 3 over 4 end exponent close parentheses squared end cell row blank equals cell 5 to the power of 3 over 4 cross times 2 end exponent end cell row blank equals cell 5 to the power of 3 over 2 end exponent end cell row blank equals cell square root of 5 cubed end root end cell end table end style 

Jadi nilai dari begin mathsize 14px style open parentheses fourth root of 5 cubed end root close parentheses squared end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 5 cubed end root end cell end table end style

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 11 Juli 2021

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Pertanyaan yang serupa

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of open parentheses fraction numerator p squared minus q squared over denominator p plus q end fraction close parentheses squared end root square root of fraction numerator p plus q over denominator p squared minus q squared end fraction end root end cell equals cell open parentheses fraction numerator p squared minus q squared over denominator p plus q end fraction close parentheses squared open parentheses fraction numerator p plus q over denominator p squared minus q squared end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator up diagonal strike open parentheses p plus q close parentheses end strike open parentheses p minus q close parentheses over denominator up diagonal strike open parentheses p plus q close parentheses end strike end fraction close parentheses squared open parentheses fraction numerator up diagonal strike open parentheses p plus q close parentheses end strike over denominator up diagonal strike open parentheses p plus q close parentheses end strike open parentheses p minus q close parentheses end fraction close parentheses end cell row blank equals cell open parentheses p minus q close parentheses to the power of up diagonal strike 2 end exponent fraction numerator 1 over denominator up diagonal strike open parentheses p minus q close parentheses end strike end fraction end cell row blank equals cell p minus q end cell end table

Jadi, jawaban yang tepat adalah E

3

Roboguru

Rasionalkan penyebut pecahan-pecachan berikut!

Pembahasan Soal:

Ingat kembali aturan berikut.

  • square root of a squared cross times b end root equals a square root of b 
  • 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 

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 5 over denominator square root of 24 end fraction end cell equals cell fraction numerator square root of 5 over denominator square root of 2 squared cross times 6 end root end fraction end cell row blank equals cell fraction numerator square root of 5 over denominator 2 square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 5 over denominator 2 square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 5 cross times 6 end root over denominator 2 cross times 6 end fraction end cell row blank equals cell fraction numerator square root of 30 over denominator 12 end fraction end cell row blank equals cell 1 over 12 square root of 30 end cell end table 

Jadi, hasil dari merasionalkan fraction numerator square root of 5 over denominator square root of 24 end fraction adalah 1 over 12 square root of 30.

0

Roboguru

Bentuk sederhana dari adalah

Pembahasan Soal:

Untuk menemukan bentuk sederhana dari open parentheses square root of 3 minus 2 close parentheses open parentheses square root of 3 plus 5 close parentheses spaceyaitu dengan mengalikan secara distributif dari open parentheses square root of 3 minus 2 close parentheses open parentheses square root of 3 plus 5 close parentheses spacesehingga diperoleh

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 3 minus 2 close parentheses open parentheses square root of 3 plus 5 close parentheses space end cell equals cell open parentheses square root of 3 cross times square root of 3 close parentheses plus open parentheses square root of 3 cross times 5 close parentheses plus open parentheses negative 2 cross times square root of 3 close parentheses plus open parentheses negative 2 cross times 5 close parentheses end cell row cell open parentheses square root of 3 minus 2 close parentheses open parentheses square root of 3 plus 5 close parentheses end cell equals cell 3 plus 5 square root of 3 minus 2 square root of 3 minus 10 end cell row cell open parentheses square root of 3 minus 2 close parentheses open parentheses square root of 3 plus 5 close parentheses end cell equals cell 3 square root of 3 minus 7 end cell end table end style


Jadi bentuk sederhana dari open parentheses square root of 3 minus 2 close parentheses open parentheses square root of 3 plus 5 close parentheses spaceadalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 square root of 3 minus 7 end cell end table

0

Roboguru

Pembahasan Soal:

2 square root of 12 cross times square root of 6 space equals space 2 square root of 12 cross times 6 end root  space space space space space space space space space space space space space space space space space space space space space space space space equals space 2 cross times square root of 72  space space space space space space space space space space space space space space space space space space space space space space space space equals space 2 square root of 36 cross times 2 end root  space space space space space space space space space space space space space space space space space space space space space space space space equals space 2 cross times 6 square root of 2  space space space space space space space space space space space space space space space space space space space space space space space space equals space 12 square root of 2

0

Roboguru

Tentukan hasil operasi bilangan berikut! d.  e.  f.  g.

Pembahasan Soal:

d. Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga 5 square root of 12 plus 4 square root of 75 diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 square root of 12 plus 4 square root of 75 end cell equals cell 5 square root of 4 cross times 3 end root minus 4 square root of 25 cross times 3 end root end cell row blank equals cell 5 square root of 2 squared cross times 3 end root minus 4 square root of 5 squared cross times 3 end root end cell row blank equals cell 5 cross times 2 square root of 3 minus 4 cross times 5 square root of 3 end cell row blank equals cell 10 square root of 3 minus 20 square root of 3 end cell end table

Berdasarkan aturan pengurangan bentuk akar dengan bilangan pokok sama yaitu a n-th root of b minus c n-th root of b equals open parentheses a minus c close parentheses n-th root of b maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 square root of 12 plus 4 square root of 75 end cell equals cell 5 square root of 4 cross times 3 end root minus 4 square root of 25 cross times 3 end root end cell row blank equals cell 5 square root of 2 squared cross times 3 end root minus 4 square root of 5 squared cross times 3 end root end cell row blank equals cell 5 cross times 2 square root of 3 minus 4 cross times 5 square root of 3 end cell row blank equals cell 10 square root of 3 minus 20 square root of 3 end cell end table

Jadi hasil dari 5 square root of 12 plus 4 square root of 75 adalah negative 10 square root of 3.

e. Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga 3 cube root of 40 plus 4 cube root of 320 minus 2 cube root of 125 diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 cube root of 40 plus 4 cube root of 320 minus 2 cube root of 125 end cell equals cell 3 cube root of 8 cross times 5 end root plus 4 cube root of 64 cross times 5 end root minus 2 cube root of 5 cubed end root end cell row blank equals cell 3 cube root of 2 cubed cross times 5 end root plus 4 cube root of 4 cubed cross times 5 end root minus 2 cube root of 5 cubed end root end cell row blank equals cell 3 cross times 2 cube root of 5 plus 4 cross times 4 cube root of 5 minus 2 cross times 5 end cell row blank equals cell 6 cube root of 5 plus 16 cube root of 5 minus 10 end cell end table

Berdasarkan aturan penjumlahan bentuk akar dengan bilangan pokok sama yaitu a n-th root of b plus c n-th root of b equals open parentheses a plus c close parentheses n-th root of b maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 cube root of 40 plus 4 cube root of 320 minus 2 cube root of 125 end cell equals cell 3 cube root of 8 cross times 5 end root plus 4 cube root of 64 cross times 5 end root minus 2 cube root of 5 cubed end root end cell row blank equals cell 3 cube root of 2 cubed cross times 5 end root plus 4 cube root of 4 cubed cross times 5 end root minus 2 cube root of 5 cubed end root end cell row blank equals cell 3 cross times 2 cube root of 5 plus 4 cross times 4 cube root of 5 minus 2 cross times 5 end cell row blank equals cell 6 cube root of 5 plus 16 cube root of 5 minus 10 end cell row blank equals cell open parentheses 6 plus 16 close parentheses cube root of 5 minus 10 end cell row blank equals cell 22 cube root of 5 minus 10 end cell end table

Jadi hasil dari 3 cube root of 40 plus 4 cube root of 320 minus 2 cube root of 125 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 22 cube root of 5 minus 10 end cell end table.

f. Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga 6 square root of 20 plus 2 square root of 75 minus 4 square root of 5 plus 3 square root of 48 diperoleh sebagai berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 6 square root of 20 plus 2 square root of 75 minus 4 square root of 5 plus 3 square root of 48 end cell equals cell 6 square root of 4 cross times 5 end root plus 2 square root of 25 cross times 3 end root minus 4 square root of 5 plus 3 square root of 16 cross times 3 end root end cell row blank equals cell 6 square root of 2 squared cross times 5 end root plus 2 square root of 5 squared cross times 3 end root minus 4 square root of 5 plus 3 square root of 4 squared cross times 3 end root end cell row blank equals cell 6 cross times 2 square root of 5 plus 2 cross times 5 square root of 3 minus 4 square root of 5 plus 3 cross times 4 square root of 3 end cell row blank equals cell 12 square root of 5 plus 10 square root of 3 minus 4 square root of 5 plus 12 square root of 3 end cell end table end style

Berdasarkan aturan penjumlahan dan pengurangan bentuk akar dengan bilangan pokok sama yaitu a n-th root of b plus-or-minus c n-th root of b equals open parentheses a plus-or-minus c close parentheses n-th root of b maka

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 6 square root of 20 plus 2 square root of 75 minus 4 square root of 5 plus 3 square root of 48 end cell equals cell 6 square root of 4 cross times 5 end root plus 2 square root of 25 cross times 3 end root minus 4 square root of 5 plus 3 square root of 16 cross times 3 end root end cell row blank equals cell 6 square root of 2 squared cross times 5 end root plus 2 square root of 5 squared cross times 3 end root minus 4 square root of 5 plus 3 square root of 4 squared cross times 3 end root end cell row blank equals cell 6 cross times 2 square root of 5 plus 2 cross times 5 square root of 3 minus 4 square root of 5 plus 3 cross times 4 square root of 3 end cell row blank equals cell 12 square root of 5 plus 10 square root of 3 minus 4 square root of 5 plus 12 square root of 3 end cell row blank equals cell 12 square root of 5 minus 4 square root of 5 plus 10 square root of 3 plus 12 square root of 3 end cell row blank equals cell open parentheses 12 minus 4 close parentheses square root of 5 plus open parentheses 10 plus 12 close parentheses square root of 3 end cell row blank equals cell 8 square root of 5 plus 22 square root of 3 end cell end table end style

Jadi hasil dari 6 square root of 20 plus 2 square root of 75 minus 4 square root of 5 plus 3 square root of 48 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 8 square root of 5 plus 22 square root of 3 end cell end table.

g. Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga 4 square root of 24 minus 5 square root of 96 plus 2 cube root of 16 plus 7 cube root of 54 diperoleh sebagai berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 square root of 24 minus 5 square root of 96 plus 2 cube root of 16 plus 7 cube root of 54 end cell equals cell 4 square root of 4 cross times 6 end root minus 5 square root of 16 cross times 6 end root plus 2 cube root of 8 cross times 2 end root plus 7 cube root of 27 cross times 2 end root end cell row blank equals cell 4 square root of 2 squared cross times 6 end root minus 5 square root of 4 squared cross times 6 end root plus 2 cube root of 2 cubed cross times 2 end root plus 7 cube root of 3 cubed cross times 2 end root end cell row blank equals cell 4 cross times 2 square root of 6 minus 5 cross times 4 square root of 6 plus 2 cross times 2 cube root of 2 plus 7 cross times 3 cube root of 2 end cell row blank equals cell 8 square root of 6 minus 20 square root of 6 plus 4 cube root of 2 plus 21 cube root of 2 end cell end table end style

Berdasarkan aturan penjumlahan dan pengurangan bentuk akar dengan bilangan pokok sama yaitu a n-th root of b plus-or-minus c n-th root of b equals open parentheses a plus-or-minus c close parentheses n-th root of b maka

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 square root of 24 minus 5 square root of 96 plus 2 cube root of 16 plus 7 cube root of 54 end cell equals cell 4 square root of 4 cross times 6 end root minus 5 square root of 16 cross times 6 end root plus 2 cube root of 8 cross times 2 end root plus 7 cube root of 27 cross times 2 end root end cell row blank equals cell 4 square root of 2 squared cross times 6 end root minus 5 square root of 4 squared cross times 6 end root plus 2 cube root of 2 cubed cross times 2 end root plus 7 cube root of 3 cubed cross times 2 end root end cell row blank equals cell 4 cross times 2 square root of 6 minus 5 cross times 4 square root of 6 plus 2 cross times 2 cube root of 2 plus 7 cross times 3 cube root of 2 end cell row blank equals cell 8 square root of 6 minus 20 square root of 6 plus 4 cube root of 2 plus 21 cube root of 2 end cell row blank equals cell open parentheses 8 minus 20 close parentheses square root of 6 plus open parentheses 4 plus 21 close parentheses cube root of 2 end cell row blank equals cell negative 12 square root of 6 plus 25 cube root of 2 end cell end table end style

Jadi hasil dari 4 square root of 24 minus 5 square root of 96 plus 2 cube root of 16 plus 7 cube root of 54 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 12 square root of 6 plus 25 cube root of 2 end cell end table.

 

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