Rasionalkan pecahan bentuk akar berikut! 1. 1/3√6 2. 6/3+√6 3.8/√5-√3

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Rasionalkan pecahan bentuk akar berikut!
1. 1/3√6
2. 6/3+√6
3.8/√5-√3

Penjelasan dengan langkah-langkah:

no 1

= frac{1}{3 sqrt{6} } times frac{3 sqrt{6} }{3 sqrt{6} } \ \ = frac{3 sqrt{6} }{9 sqrt{36} } \ \ = frac{3 sqrt{6} }{9(6)} \ \ = frac{ sqrt{6} }{3(6)} \ \ = frac{ sqrt{6} }{18}

no 2

= frac{6}{3 + sqrt{6} } times frac{3 - sqrt{6} }{3 - sqrt{6} } \ \ = frac{6(3 - sqrt{6} )}{ {3}^{2} - sqrt{ {6}^{2} } } \ \ = frac{18 - 6 sqrt{6} }{9 - 6} \ \ = frac{6( 3- sqrt{6} )}{3} \ \ = 2(3 - sqrt{6} ) \ \ = 6 - 2 sqrt{6}

no 3

= frac{8}{ sqrt{5} - sqrt{3} } times frac{ sqrt{5} + sqrt{3} }{ sqrt{5} + sqrt{3} } \ \ = frac{8( sqrt{5} + sqrt{3} )}{ sqrt{ {5}^{2} } - sqrt{ {3}^{2} } } \ \ = frac{8( sqrt{5} + sqrt{3}) }{5 - 3} \ \ = frac{8( sqrt{5} + sqrt{3} )}{2} \ \ = 4( sqrt{5} + sqrt{3} ) \ \ = 4 sqrt{5} + 4 sqrt{3}