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Tentukan hasil perkalian akar bilangan berikut! d. 4 2 ​ ( 24 ​ − 4 4 ​ )

Tentukan hasil perkalian akar bilangan berikut!
d.    

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

hasil dari adalah .

hasil dari 4 square root of 2 left parenthesis square root of 24 minus fourth root of 4 right parenthesis adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 16 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table.

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Pembahasan

Ingat kembali sifat perkalian dan penjumlahan akar berikut. Dengan rumus di atas diperoleh perhitungan sebagai berikut. Jadi, hasil dari adalah .

Ingat kembali sifat perkalian dan penjumlahan akar berikut.

  • square root of a left parenthesis square root of b plus square root of c right parenthesis equals square root of a times square root of b plus square root of a times square root of c  
  • square root of a times square root of b equals square root of a times b end root 
  • square root of a squared times b end root equals a square root of b 
  • m-th root of a to the power of n end root equals a to the power of n over m end exponent 
  • a to the power of n times a to the power of m equals a to the power of n plus m end exponent 

Dengan rumus di atas diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 square root of 2 left parenthesis square root of 24 minus fourth root of 4 right parenthesis end cell equals cell 4 square root of 2 times square root of 24 minus 4 square root of 2 times fourth root of 4 end cell row blank equals cell 4 square root of 2 times 24 end root minus 4 times square root of 2 times fourth root of 2 squared end root end cell row blank equals cell 4 square root of 48 minus 4 times 2 to the power of 1 half end exponent times 2 to the power of 2 over 4 end exponent end cell row blank equals cell 4 square root of 4 squared times 3 end root minus 4 times 2 to the power of 1 half plus 2 over 4 end exponent end cell row blank equals cell 4 times 4 square root of 3 minus 4 times 2 to the power of 1 half plus 1 half end exponent end cell row blank equals cell 16 square root of 3 minus 4 times 2 to the power of 1 end cell row blank equals cell 16 square root of 3 minus 8 end cell end table 

Jadi, hasil dari 4 square root of 2 left parenthesis square root of 24 minus fourth root of 4 right parenthesis adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 16 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table.

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