Roboguru

Sederhanakanlah bentuk akar di bawah ini! c.

Pertanyaan

Sederhanakanlah bentuk akar di bawah ini!

c. 2 square root of 5 cross times open parentheses 2 square root of 120 plus 5 square root of 24 close parentheses 

Pembahasan Soal:

Ingat kembali sifat bentuk akar berikut.

a square root of b cross times open parentheses c square root of d plus e square root of f close parentheses equals a c square root of b d end root plus a e square root of b f end root

Sehingga dapat ditentukan bentuk sederhana dari bentuk akar di atas sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row p equals cell 2 square root of 5 cross times open parentheses 2 square root of 120 plus 5 square root of 24 close parentheses end cell row blank equals cell open parentheses 2 square root of 5 cross times 2 square root of 120 close parentheses plus open parentheses 2 square root of 5 cross times 5 square root of 24 close parentheses end cell row blank equals cell open parentheses 2 cross times 2 cross times square root of 5 cross times 120 end root close parentheses plus open parentheses 2 cross times 5 cross times square root of 5 cross times 24 end root close parentheses end cell row blank equals cell open parentheses 4 square root of 5 cross times 5 cross times 4 cross times 6 end root close parentheses plus open parentheses 10 square root of 5 cross times 4 cross times 6 end root close parentheses end cell row blank equals cell open parentheses 4 cross times 5 cross times 2 cross times square root of 6 close parentheses plus open parentheses 10 cross times 2 cross times square root of 6 cross times square root of 5 close parentheses end cell row blank equals cell 40 square root of 6 plus open parentheses 20 square root of 6 cross times square root of 5 close parentheses end cell row blank equals cell 20 square root of 6 open parentheses 2 plus square root of 5 close parentheses end cell end table   

Dengan demikian, diperoleh bentuk sederhana dari bentuk akar 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 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 square root of 120 plus 5 square root of 24 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 20 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 6 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 plus square root of 5 close parentheses end cell end table.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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