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Bentuk rasional dari 17 + 2 60 5 + 3 adalah ....

Bentuk rasional dari $\frac{5 + 3}{17 + 2 60}$ adalah ....

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Ingat bahwa dan Sehingga diperoleh

Ingat bahwa

dan $begin mathsize 14px style fraction numerator 1 over denominator square root of italic a plus square root of italic b end fraction equals fraction numerator 1 over denominator square root of italic a plus square root of italic b end fraction cross times fraction numerator square root of italic a minus sign square root of italic b over denominator square root of italic a minus sign square root of italic b end fraction end style$

Sehingga diperoleh

$begin mathsize 14px style fraction numerator square root of 5 plus square root of 3 over denominator square root of 17 plus 2 square root of 60 end root end fraction equals fraction numerator square root of 5 plus square root of 3 over denominator square root of left parenthesis 12 plus 5 right parenthesis plus 2 square root of left parenthesis 12 cross times 5 right parenthesis end root end root end fraction equals fraction numerator square root of 5 plus square root of 3 over denominator square root of 12 plus square root of 5 end fraction equals fraction numerator square root of 5 plus square root of 3 over denominator 3 square root of 3 plus square root of 5 end fraction equals fraction numerator square root of 5 plus square root of 3 over denominator 3 square root of 3 plus square root of 5 end fraction cross times fraction numerator 3 square root of 3 minus sign square root of 5 over denominator 3 square root of 3 minus sign square root of 5 end fraction equals fraction numerator open parentheses square root of 5 plus square root of 3 close parentheses open parentheses 3 square root of 3 minus sign square root of 5 close parentheses over denominator open parentheses 3 square root of 3 plus square root of 5 close parentheses open parentheses 3 square root of 3 minus sign square root of 5 close parentheses end fraction equals fraction numerator square root of 5 open parentheses 3 square root of 3 minus sign square root of 5 close parentheses plus square root of 3 open parentheses 3 square root of 3 minus sign square root of 5 close parentheses over denominator open parentheses 3 square root of 3 close parentheses squared minus sign open parentheses square root of 5 close parentheses squared end fraction equals fraction numerator 3 square root of 15 minus sign 5 plus 3.3 minus sign square root of 15 over denominator 27 minus sign 5 end fraction equals fraction numerator 3 square root of 15 minus sign 5 plus 9 minus sign square root of 15 over denominator 22 end fraction equals fraction numerator negative sign 5 plus 9 plus 3 square root of 15 minus sign square root of 15 over denominator 22 end fraction equals fraction numerator 4 plus 2 square root of 15 over denominator 22 end fraction equals fraction numerator 2 open parentheses 2 plus square root of 15 close parentheses over denominator 22 end fraction equals fraction numerator 2 plus square root of 15 over denominator 11 end fraction equals 1 over 11 left parenthesis 2 plus square root of 15 right parenthesis end style$