Pertanyaan

Tentukan hasil operasi bilanganberikut! d. 5 12 ​ + 4 75 ​ e. 3 3 40 ​ + 4 3 320 ​ − 2 3 125 ​ f. 6 20 ​ + 2 75 ​ − 4 5 ​ + 3 48 ​ g. 4 24 ​ − 5 96 ​ + 2 3 16 ​ + 7 3 54 ​

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

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

d. Jika dapat difaktorkan menjadi dengan bilangan berpangkat maka dapat disederhanakan sehingga diperoleh sebagai berikut. Berdasarkan aturan pengurangan bentuk akar dengan bilangan pokok sama yaitu maka Jadi hasil dari adalah . e.Jika dapat difaktorkan menjadi dengan bilangan berpangkat maka dapat disederhanakan sehingga diperoleh sebagai berikut. Berdasarkan aturan penjumlahanbentuk akar dengan bilangan pokok sama yaitu maka Jadi hasil dari adalah . f.Jika dapat difaktorkan menjadi dengan bilangan berpangkat maka dapat disederhanakan sehingga diperoleh sebagai berikut. Berdasarkan aturan penjumlahan dan penguranganbentuk akar dengan bilangan pokok sama yaitu maka Jadi hasil dari adalah . g.Jika dapat difaktorkan menjadi dengan bilangan berpangkat maka dapat disederhanakan sehingga diperoleh sebagai berikut. Berdasarkan aturan penjumlahan dan penguranganbentuk akar dengan bilangan pokok sama yaitu maka Jadi hasil dari adalah .

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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