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Bentuk sederhana dari  adalah...

Pertanyaan

Bentuk sederhana dari fraction numerator 2 square root of 3 over denominator square root of 6 minus square root of 3 end fraction adalah...space 

Pembahasan Soal:

Pecahan yang penyebutnya berbentuk akar dapat disederhanakan dengan cara merasionalkannya yaitu mengalikannya dengan akar sekawan. Perhatikan penghitungan berikut!

 fraction numerator 2 square root of 3 over denominator square root of 6 minus square root of 3 end fraction equals fraction numerator 2 square root of 3 over denominator square root of 6 minus square root of 3 end fraction cross times fraction numerator square root of 6 plus square root of 3 over denominator square root of 6 plus square root of 3 end fraction fraction numerator 2 square root of 3 over denominator square root of 6 minus square root of 3 end fraction equals fraction numerator 2 square root of 18 plus 2 square root of 9 over denominator 6 minus 3 end fraction fraction numerator 2 square root of 3 over denominator square root of 6 minus square root of 3 end fraction equals fraction numerator 2 open parentheses square root of 9 cross times 2 end root plus square root of 9 close parentheses over denominator 3 end fraction fraction numerator 2 square root of 3 over denominator square root of 6 minus square root of 3 end fraction equals fraction numerator 2 open parentheses 3 square root of 2 plus 3 close parentheses over denominator 3 end fraction fraction numerator 2 square root of 3 over denominator square root of 6 minus square root of 3 end fraction equals fraction numerator 6 open parentheses square root of 2 plus 1 close parentheses over denominator 3 end fraction fraction numerator 2 square root of 3 over denominator square root of 6 minus square root of 3 end fraction equals 2 open parentheses square root of 2 plus 1 close parentheses  Catatan colon open parentheses a plus b close parentheses open parentheses a minus b close parentheses equals a squared minus b squared open parentheses square root of 6 minus square root of 3 close parentheses open parentheses square root of 6 plus square root of 3 close parentheses equals open parentheses square root of 6 close parentheses squared minus open parentheses square root of 3 close parentheses squared open parentheses square root of 6 minus square root of 3 close parentheses open parentheses square root of 6 plus square root of 3 close parentheses equals 6 minus 3 open parentheses square root of 6 minus square root of 3 close parentheses open parentheses square root of 6 plus square root of 3 close parentheses equals 3 

Jadi, bentuk sederhana dari fraction numerator 2 square root of 3 over denominator square root of 6 minus square root of 3 end fraction adalah 2 open parentheses square root of 2 plus 1 close parentheses. 

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Terakhir diupdate 18 Mei 2021

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