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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. 

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R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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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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