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Pertanyaan

Hasil dari open parentheses 4 a square root of 3 minus 3 close parentheses squared equals....

  1. 48 a squared minus 12 a square root of 3 plus 9

  2. 48 a squared minus 12 a square root of 3 minus 9

  3. 48 a squared minus 24 a square root of 3 plus 9

  4. 48 a squared minus 24 a square root of 3 minus 9

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat rumus pengkuadratan suku dua bentuk aljabar yaitu

open parentheses a minus b close parentheses squared equals a squared minus 2 a b plus b squared

Sehingga open parentheses 4 a square root of 3 minus 3 close parentheses squared diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 a square root of 3 minus 3 close parentheses squared end cell equals cell open parentheses 4 a square root of 3 close parentheses squared minus 2 open parentheses 4 a square root of 3 close parentheses open parentheses 3 close parentheses plus 3 squared end cell row blank equals cell open parentheses 4 a square root of 3 close parentheses squared minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell end table

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma space a not equal to 0 sehingga diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 a square root of 3 minus 3 close parentheses squared end cell equals cell open parentheses 4 a square root of 3 close parentheses squared minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell row blank equals cell open parentheses 4 a cross times 3 to the power of 1 half end exponent close parentheses squared minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell end table

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 a square root of 3 minus 3 close parentheses squared end cell equals cell open parentheses 4 a square root of 3 close parentheses squared minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell row blank equals cell open parentheses 4 a cross times 3 to the power of 1 half end exponent close parentheses squared minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell row blank equals cell 4 squared cross times a squared cross times open parentheses 3 to the power of 1 half end exponent close parentheses squared minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell row blank equals cell 16 a squared open parentheses 3 to the power of 1 half end exponent close parentheses squared minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 a square root of 3 minus 3 close parentheses squared end cell equals cell 16 a squared open parentheses 3 to the power of 1 half end exponent close parentheses squared minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell row blank equals cell 16 a squared cross times 3 to the power of 1 half cross times 2 end exponent minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell row blank equals cell 16 a squared cross times 3 to the power of 1 minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell end table

Berdasarkan sifat bilangan berpangkat a to the power of 1 equals a sehingga diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 a square root of 3 minus 3 close parentheses squared end cell equals cell 16 a squared cross times 3 to the power of 1 minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell row blank equals cell 16 a squared cross times 3 minus 6 open parentheses 4 a square root of 3 close parentheses plus 9 end cell row blank equals cell 48 a squared minus 24 a square root of 3 plus 9 end cell end table

Jadi Hasil dari open parentheses 4 a square root of 3 minus 3 close parentheses squared adalah 48 a squared minus 24 a square root of 3 plus 9.

Oleh karena itu, jawaban yang benar adalah C.

75

5.0 (2 rating)

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