Pertanyaan

Bentuk rasional dari ( 7 − 48 ) − 2 15 + 2 adalah ....

Bentuk rasional dari $\frac{15 + 2}{( 7 - 48 ) - 2}$ adalah ....

$begin mathsize 14px style fraction numerator 3 square root of 5 minus square root of 2 over denominator 3 end fraction end style$
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 5 plus 2 square root of 2 over denominator 3 end fraction end cell end table end style$
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 5 plus square root of 2 over denominator 3 end fraction end cell end table end style$

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Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa Jadi, bentuk rasional dari adalah . Dengan demikian, jawaban yang tepat adalah D.

Perhatikan bahwa

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 15 plus square root of 2 over denominator left parenthesis square root of 7 minus square root of 48 end root right parenthesis minus 2 end fraction end cell equals cell fraction numerator square root of 15 plus square root of 2 over denominator left parenthesis square root of 7 minus square root of 4 cross times 12 end root end root right parenthesis minus 2 end fraction end cell row blank equals cell fraction numerator square root of 15 plus square root of 2 over denominator left parenthesis square root of 7 minus 2 square root of 12 end root right parenthesis minus 2 end fraction end cell row blank equals cell fraction numerator square root of 15 plus square root of 2 over denominator left parenthesis square root of left parenthesis 4 plus 3 right parenthesis minus 2 square root of 4 cross times 3 end root end root right parenthesis minus 2 end fraction end cell row blank equals cell fraction numerator square root of 15 plus square root of 2 over denominator left parenthesis square root of 4 minus square root of 3 right parenthesis minus 2 end fraction end cell row blank equals cell fraction numerator square root of 15 plus square root of 2 over denominator left parenthesis 2 minus square root of 3 right parenthesis minus 2 end fraction end cell row blank equals cell fraction numerator square root of 15 plus square root of 2 over denominator negative square root of 3 end fraction end cell row blank equals cell negative fraction numerator square root of 15 plus square root of 2 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell negative fraction numerator left parenthesis square root of 15 cross times square root of 3 right parenthesis plus left parenthesis square root of 2 cross times square root of 3 right parenthesis over denominator 3 end fraction end cell row blank equals cell negative fraction numerator square root of 45 plus square root of 6 over denominator 3 end fraction end cell row blank equals cell negative fraction numerator square root of 9 cross times 5 end root plus square root of 2 over denominator 3 end fraction end cell row blank equals cell negative fraction numerator 3 square root of 5 plus square root of 2 over denominator 3 end fraction end cell end table end style$

Jadi, bentuk rasional dari $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 15 plus square root of 2 over denominator left parenthesis square root of 7 minus square root of 48 end root right parenthesis minus 2 end fraction end cell end table end style$ adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 square root of 5 plus square root of 2 over denominator 3 end fraction end cell end table end style$ .

Dengan demikian, jawaban yang tepat adalah D.

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