Question

Como racionaalizo uma fracao com raiz quadrada no denominador e numerador ? Racionalizem essa pra mim , 5v15/v50

Answer 1

$Simplificando:\\\\ \dfrac{5\sqrt{15}}{\sqrt{50}}=\dfrac{5\sqrt{15}}{\sqrt{2 \times 5 \times 5}}=\dfrac{5\sqrt{15}}{\sqrt{2 \times 5^2}}=\dfrac{5\sqrt{15}}{5\sqrt{2}}\\\\\\ Racionalizando:\\\\ \dfrac{5\sqrt{15}}{5\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{5\sqrt{15 \times 2}}{5\sqrt{2\times2}}=\dfrac{5\sqrt{30}}{5\sqrt{2^2}}=\dfrac{5\sqrt{30}}{5\times2}}=\dfrac{5\sqrt{30}}{10}\\\\\\ Simplificando\ novamente:\\\\ \dfrac{5\sqrt{30}}{10}\ \ \boxed{=\dfrac{\sqrt{30}}{2}}$

Bons estudos!