Question

QUERIA OS CÁLCULOS, FIQUEI TENTANDO FAZER MUITAS VEZES MAIS NÃO CONSEGUIR CHEGA AO RESULTADO CERTO.
DESDE JÁ AGRADEÇO

Answer 1

a) $\dfrac{\sqrt{12}\cdot \sqrt{15}}{\sqrt{8}}$

$=\dfrac{\sqrt{12\cdot 15}}{\sqrt{8}}\\ \\ =\dfrac{\sqrt{180}}{\sqrt{8}}\\ \\ =\dfrac{\sqrt{2^{2}\cdot 3^{2}\cdot 5}}{\sqrt{2^{2}\cdot 2}}\\ \\ =\dfrac{\sqrt{2^{2}}\cdot\sqrt{3^{2}}\cdot \sqrt{5}}{\sqrt{2^{2}}\cdot \sqrt{2}}\\ \\ =\dfrac{\diagup\!\!\!\! 2\cdot 3\cdot \sqrt{5}}{\diagup\!\!\!\! 2\cdot \sqrt{2}}\\ \\ =\dfrac{3\cdot \sqrt{5}}{\sqrt{2}}\\ \\ =\dfrac{3\cdot \sqrt{5}}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}\\ \\ =\dfrac{3\cdot \sqrt{5} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}}\\ \\ =\dfrac{3 \cdot \sqrt{5 \cdot 2}}{\sqrt{2 \cdot 2}}\\ \\ =\dfrac{3\sqrt{10}}{2}$


b) $\dfrac{\sqrt[3]{9}\cdot \sqrt[3]{10}}{\sqrt[3]{12}\cdot \sqrt[3]{15}}$

$=\dfrac{\sqrt[3]{9 \cdot 10}}{\sqrt[3]{12 \cdot 15}}\\ \\ =\dfrac{\sqrt[3]{90}}{\sqrt[3]{180}}\\ \\ =\sqrt[3]{\dfrac{90}{180}}\\ \\ =\sqrt[3]{\dfrac{90 \div 90}{180 \div 90}}\\ \\ =\sqrt[3]{\dfrac{1}{2}}\\ \\ =\dfrac{\sqrt[3]{1}}{\sqrt[3]{2}}\\ \\ =\dfrac{1}{\sqrt[3]{2}}\\ \\ =\dfrac{1}{\sqrt[3]{2}}\cdot \dfrac{\sqrt[3]{2^{2}}}{\sqrt[3]{2^{2}}}\\ \\ =\dfrac{1\cdot \sqrt[3]{2^{2}}}{\sqrt[3]{2}\cdot \sqrt[3]{2^{2}}}\\ \\ =\dfrac{\sqrt[3]{4}}{\sqrt[3]{2^{1} \cdot 2^{2}}}\\ \\ =\dfrac{\sqrt[3]{4}}{\sqrt[3]{2^{1+2}}}\\ \\ =\dfrac{\sqrt[3]{4}}{\sqrt[3]{2^{3}}}\\ \\ =\dfrac{\sqrt[3]{4}}{2}$


c) $\dfrac{\sqrt[6]{4}\cdot \sqrt[3]{\sqrt{10}}}{\sqrt[6]{120}}$

$=\dfrac{\sqrt[6]{4}\cdot \sqrt[3\,\cdot\,2]{10}}{\sqrt[6]{120}}\\ \\ =\dfrac{\sqrt[6]{4}\cdot \sqrt[6]{10}}{\sqrt[6]{120}}\\ \\ =\dfrac{\sqrt[6]{4\cdot 10}}{\sqrt[6]{120}}\\ \\ =\dfrac{\sqrt[6]{40}}{\sqrt[6]{120}}\\ \\ =\sqrt[6]{\dfrac{40}{120}}\\ \\ =\sqrt[6]{\dfrac{40 \div 40}{120 \div 40}}\\ \\ =\sqrt[6]{\dfrac{1}{30}}\\ \\ \dfrac{\sqrt[6]{1}}{\sqrt[6]{3}}\\ \\ =\dfrac{1}{\sqrt[6]{3}}$