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Tentukan hasil perkalian akar bilangan berikut! b. 2 ​ ( 6 ​ + 2 4 4 ​ )

Tentukan hasil perkalian akar bilangan berikut!
b.   

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

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hasil dari adalah .

hasil dari square root of 2 left parenthesis square root of 6 plus 2 fourth root of 4 right parenthesis adalah 2 square root of 3 plus 4.

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 square root of 2 left parenthesis square root of 6 plus 2 fourth root of 4 right parenthesis end cell equals cell square root of 2 times square root of 6 plus square root of 2 times 2 fourth root of 4 end cell row blank equals cell square root of 2 times 6 end root plus 2 times square root of 2 times fourth root of 2 squared end root end cell row blank equals cell square root of 12 plus 2 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 square root of 2 squared times 3 end root plus 2 times 2 to the power of 1 half plus 2 over 4 end exponent end cell row blank equals cell 2 square root of 3 plus 2 times 2 to the power of 1 half plus 1 half end exponent end cell row blank equals cell 2 square root of 3 plus 2 times 2 to the power of 1 end cell row blank equals cell 2 square root of 3 plus 2 times 2 end cell row blank equals cell 2 square root of 3 plus 4 end cell end table 

Jadi, hasil dari square root of 2 left parenthesis square root of 6 plus 2 fourth root of 4 right parenthesis adalah 2 square root of 3 plus 4.

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