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Sederhanakan akar-akar bilangan berikut! d. 41+610​​−54+145​​

Pertanyaan

Sederhanakan akar-akar bilangan berikut!

d. square root of 41 plus 6 square root of 10 end root minus square root of 54 plus 14 square root of 5 end root

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

bentuk sederhana dari square root of 47 plus 6 square root of 10 end root minus square root of 54 plus 14 square root of 5 end root adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 square root of 5 minus 5 end cell end table.

Pembahasan

d. Diketahui square root of 41 plus 6 square root of 10 end root minus square root of 54 plus 14 square root of 5 end root maka square root of 41 plus 6 square root of 10 end root tidak dapat disederhanakan dengan akar bersarang dapat dikerjakan jika diasumsikan square root of 47 plus 6 square root of 10 end root sehingga diperoleh sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 47 plus 6 square root of 10 end root end cell equals cell square root of 47 plus 2 cross times 3 square root of 10 end root end cell row blank equals cell square root of 47 plus 2 square root of 3 squared cross times 10 end root end root end cell row blank equals cell square root of 47 plus 2 square root of 9 cross times 10 end root end root end cell row blank equals cell square root of 47 plus square root of 90 end root end cell row blank equals cell square root of open parentheses 45 plus 2 close parentheses plus 2 square root of 45 cross times 2 end root end root end cell row blank equals cell square root of 45 plus square root of 2 end cell end table

Sedangkan square root of 54 plus 14 square root of 5 end root diperoleh sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 54 plus 14 square root of 5 end root end cell equals cell square root of 54 plus 2 cross times 7 square root of 5 end root end cell row blank equals cell square root of 54 plus 2 square root of 7 squared cross times 5 end root end root end cell row blank equals cell square root of 54 plus 2 square root of 49 cross times 5 end root end root end cell row blank equals cell square root of open parentheses 49 plus 5 close parentheses plus 2 square root of 49 cross times 5 end root end root end cell row blank equals cell square root of 49 plus square root of 5 end cell row blank equals cell 7 plus square root of 5 end cell end table

Sehingga square root of 47 plus 6 square root of 10 end root minus square root of 54 plus 14 square root of 5 end root diperoleh sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 47 plus 6 square root of 10 end root minus square root of 54 plus 14 square root of 5 end root end cell equals cell square root of 45 plus 2 minus open parentheses 7 plus square root of 5 close parentheses end cell row blank equals cell square root of 9 cross times 5 end root plus 2 minus 7 minus square root of 5 end cell row blank equals cell square root of 3 squared cross times 5 end root minus 5 minus square root of 5 end cell row blank equals cell 3 square root of 5 minus square root of 5 minus 5 end cell row blank equals cell open parentheses 3 minus 1 close parentheses square root of 5 minus 5 end cell row blank equals cell 2 square root of 5 minus 5 end cell end table

Jadi bentuk sederhana dari square root of 47 plus 6 square root of 10 end root minus square root of 54 plus 14 square root of 5 end root adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 square root of 5 minus 5 end cell end table.

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