Rasionalkan 4−221

Pertanyaan

Rasionalkan $begin mathsize 14px style 4 minus fraction numerator 1 over denominator 2 square root of 2 end fraction end style$

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

bentuk rasional dari $begin mathsize 14px style 4 minus fraction numerator 1 over denominator 2 square root of 2 end fraction end style$ adalah $begin mathsize 14px style 4 minus fraction numerator square root of 2 over denominator 4 end fraction end style$ .

Pembahasan

Diperhatikan bahwa

$begin mathsize 14px style 4 minus fraction numerator 1 over denominator 2 square root of 2 end fraction equals fraction numerator 8 square root of 2 minus 1 over denominator 2 square root of 2 end fraction end style$

Selanjutnya bentuk $begin mathsize 14px style fraction numerator 8 square root of 2 minus 1 over denominator 2 square root of 2 end fraction end style$ dapat dirasionalkan dengan mengalikan pembilang dan penyebut dengan sekawan dari , yaitu . Sehingga diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 8 square root of 2 minus 1 over denominator 2 square root of 2 end fraction end cell equals cell fraction numerator 8 square root of 2 minus 1 over denominator 2 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator open parentheses 8 square root of 2 minus 1 close parentheses times square root of 2 over denominator 2 times open parentheses square root of 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator 16 minus square root of 2 over denominator 4 end fraction end cell row blank equals cell 4 minus fraction numerator square root of 2 over denominator 4 end fraction end cell end table end style$

Jadi, bentuk rasional dari $begin mathsize 14px style 4 minus fraction numerator 1 over denominator 2 square root of 2 end fraction end style$ adalah $begin mathsize 14px style 4 minus fraction numerator square root of 2 over denominator 4 end fraction end style$ .