Bentuk sederhana dari 22​−5​9​ = ...

Pertanyaan

Bentuk sederhana dari begin mathsize 12px style fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction end style = ...

  1. begin mathsize 12px style 6 square root of 2 plus 3 square root of 5 end style

  2. begin mathsize 12px style 9 square root of 2 plus 9 square root of 5 end style

  3. begin mathsize 12px style 12 square root of 2 plus square root of 5 end style

  4. begin mathsize 12px style 18 square root of 2 plus square root of 5 end style

  5. begin mathsize 12px style 18 square root of 2 plus 9 square root of 5 end style

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

 begin mathsize 12px style fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction equals 6 square root of 2 plus 3 square root of 5 end style

Pembahasan

Penyederhanaan bentuk akar dapat dilakukan dengan mengalikan bentuk akar tersebut dengan akar sekawan

begin mathsize 12px style fraction numerator a over denominator b square root of b minus square root of c end fraction  equals fraction numerator a over denominator b square root of b minus square root of c end fraction cross times fraction numerator open parentheses b square root of b plus square root of c close parentheses over denominator open parentheses b square root of b plus square root of c close parentheses end fraction  equals fraction numerator a open parentheses b square root of b plus square root of c close parentheses over denominator b cubed minus c end fraction    fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction  equals fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction cross times fraction numerator open parentheses 2 square root of 2 plus square root of 5 close parentheses over denominator open parentheses 2 square root of 2 plus square root of 5 close parentheses end fraction  equals fraction numerator 18 square root of 2 plus 9 square root of 5 over denominator 4 cross times 2 minus 5 end fraction  equals fraction numerator 18 square root of 2 plus 9 square root of 5 over denominator 8 minus 5 end fraction  equals fraction numerator 18 square root of 2 plus 9 square root of 5 over denominator 3 end fraction  equals 6 square root of 2 plus 3 square root of 5 end style

Jadi, begin mathsize 12px style fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction equals 6 square root of 2 plus 3 square root of 5 end style

60

3.0 (4 rating)

Muhammad Hafzillah

Jawaban tidak sesuai

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