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Pertanyaan

Tentukan hasil operasi akar-akar bilangan berikut!

e. fraction numerator 5 square root of 8 cross times 4 square root of 15 over denominator 10 square root of 6 end fraction                  

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

hasil dari fraction numerator 5 square root of 8 cross times 4 square root of 15 over denominator 10 square root of 6 end fraction adalah 4 square root of 5.

Pembahasan

Ingat kembali sifat perkalian dan pembagian akar berikut!

Jika a space dan space b sebarang bilangan bulat, maka berlaku:

square root of a cross times square root of b equals square root of a cross times b end root   

fraction numerator square root of a over denominator square root of b end fraction equals square root of a over b end root 

Dengan rumus di atas, diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 square root of 8 cross times 4 square root of 15 over denominator 10 square root of 6 end fraction end cell equals cell fraction numerator left parenthesis 5 cross times 4 right parenthesis left parenthesis square root of 8 cross times square root of 15 right parenthesis over denominator 10 square root of 6 end fraction end cell row blank equals cell fraction numerator 20 square root of 8 cross times 15 end root over denominator 10 square root of 6 end fraction end cell row blank equals cell fraction numerator 20 square root of 120 over denominator 10 square root of 6 end fraction end cell row blank equals cell 20 over 10 cross times square root of 120 over 6 end root end cell row blank equals cell 2 cross times square root of 20 end cell row blank equals cell 2 cross times square root of 4 cross times 5 end root end cell row blank equals cell 2 cross times 2 square root of 5 end cell row blank equals cell 4 square root of 5 end cell end table                       

Jadi, hasil dari fraction numerator 5 square root of 8 cross times 4 square root of 15 over denominator 10 square root of 6 end fraction adalah 4 square root of 5.

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