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Jika a, b, dan c bilangan bulat dan a50​+b12​+c80​=152​+103​+85​, maka nilai dari c2(a+b)​ adalah ….

Pertanyaan

Jika a, b, dan c bilangan bulat dan begin mathsize 14px style a square root of 50 plus b square root of 12 plus c square root of 80 equals 15 square root of 2 plus 10 square root of 3 plus 8 square root of 5 end style, maka nilai dari begin mathsize 14px style c-th root of 2 open parentheses a plus b close parentheses end root end style adalah ….space 

  1. begin mathsize 14px style square root of 2 end style 

  2. begin mathsize 14px style 2 square root of 2 end style 

  3. begin mathsize 14px style 4 end style 

  4. begin mathsize 14px style 16 end style 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a square root of 50 plus b square root of 12 plus c square root of 80 end cell equals cell 15 square root of 2 plus 10 square root of 3 plus 8 square root of 5 end cell row cell a square root of 25 cross times 2 end root plus b square root of 4 cross times 3 end root plus c square root of 16 cross times 5 end root end cell equals cell 15 square root of 2 plus 10 square root of 3 plus 8 square root of 5 end cell row cell a cross times 5 square root of 2 plus b cross times 2 square root of 3 plus c cross times 4 square root of 5 end cell equals cell 15 square root of 2 plus 10 square root of 3 plus 8 square root of 5 end cell row cell 5 a square root of 2 plus 2 b square root of 3 plus 4 c square root of 5 end cell equals cell 15 square root of 2 plus 10 square root of 3 plus 8 square root of 5 end cell end table end style 

Karena a,b,dan c bilangan bulat, maka didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 5 a end cell equals 15 row a equals 3 end table end style 

Kemudian

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 b end cell equals 10 row b equals 5 end table end style 

Dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 c end cell equals 8 row c equals 2 end table end style 

Dengan demikian,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c-th root of 2 open parentheses a plus b close parentheses end root end cell equals cell square root of 2 open parentheses 3 plus 5 close parentheses end root end cell row blank equals cell square root of 2 open parentheses 8 close parentheses end root end cell row blank equals cell square root of 16 end cell row blank equals 4 end table end style 

Jadi, jawaban yang tepat adalah C.

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