Question

Simplifique a expressão: 3√125/5-4√5

Answer 1

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Solução!

$\dfrac{3 \sqrt{125} }{5-4 \sqrt{5} }\\\\\\\ \dfrac{3 .5\sqrt{5} }{5-4 \sqrt{5} }\\\\\\\ \dfrac{15\sqrt{5} }{5-4 \sqrt{5} }\\\\\\\ Racionalizando~~o~~denominador~~fica ~~assim!\\\\\\\ \dfrac{15\sqrt{5} }{5-4 \sqrt{5} } \times \dfrac{5+4 \sqrt{5} }{5+4 \sqrt{5} }$



$\dfrac{75 \sqrt{5}+300 }{25+20 \sqrt{5}-20 \sqrt{5}-16.5}\\\\\\\\ \dfrac{75 \sqrt{5}+60.5 }{25-80}\\\\\\\\ \dfrac{75 \sqrt{5}+300 }{25+20 \sqrt{5}-20 \sqrt{5}-16.5}\\\\\\\\ \dfrac{75 \sqrt{5}+300 }{-55}$


$\dfrac{5 (15\sqrt{5}+60) }{-55} \\\\\\\\ \boxed{-\dfrac{ (15\sqrt{5}+60) }{11}}$

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