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Tentukan hasil penjumlahan dari pecahan berikut! 5​3​+3​2​

Pertanyaan

Tentukan hasil penjumlahan dari pecahan berikut!

fraction numerator 3 over denominator square root of 5 end fraction plus fraction numerator 2 over denominator square root of 3 end fraction

 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

diperoleh table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 over denominator square root of 5 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 over denominator square root of 3 end fraction 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 cell fraction numerator 9 square root of 5 plus 10 square root of 3 over denominator 15 end fraction end cell end table.

Pembahasan

Untuk merasionalkan penyebut pecahan berbentuk fraction numerator a over denominator square root of b end fraction dapat dilakukan dengan rumus dan prosedur sebagai berikut.

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

Sehingga penjumlahan pecahan  fraction numerator 3 over denominator square root of 5 end fraction plus fraction numerator 2 over denominator square root of 3 end fraction dapat ditentukan hasilnya dengan terlebih dahulu menyamakan penyebutnya, kemudian dilakukan rasionalisasi penyebut pecahan, seperti ditunjukkan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 over denominator square root of 5 end fraction plus fraction numerator 2 over denominator square root of 3 end fraction end cell equals cell fraction numerator 3 cross times square root of 3 over denominator square root of 15 end fraction plus fraction numerator 2 cross times square root of 5 over denominator square root of 15 end fraction end cell row blank equals cell fraction numerator 3 square root of 3 plus 2 square root of 5 over denominator square root of 15 end fraction end cell row blank equals cell fraction numerator 3 square root of 3 plus 2 square root of 5 over denominator square root of 15 end fraction cross times fraction numerator square root of 15 over denominator square root of 15 end fraction end cell row blank equals cell fraction numerator 3 square root of 3 cross times 15 end root plus 2 square root of 5 cross times 15 end root over denominator open parentheses square root of 15 close parentheses squared end fraction end cell row blank equals cell fraction numerator 3 square root of 45 plus 2 square root of 75 over denominator 15 end fraction end cell row blank equals cell fraction numerator open parentheses 3 cross times 3 square root of 5 close parentheses plus open parentheses 2 cross times 5 square root of 3 close parentheses over denominator 15 end fraction end cell row blank equals cell fraction numerator 9 square root of 5 plus 10 square root of 3 over denominator 15 end fraction end cell end table 

Dengan demikian, diperoleh table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 over denominator square root of 5 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 over denominator square root of 3 end fraction 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 cell fraction numerator 9 square root of 5 plus 10 square root of 3 over denominator 15 end fraction end cell end table.

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