Question

Qual a raiz cúbica de 28 x raiz quadrada de 98

Answer 1

Olá, Rosemarirb.

$\sqrt[3]{28}\times\sqrt{98}=\sqrt[6]{28^2}\times\sqrt[6]{98^3}=\sqrt[6]{28^2\cdot98^3}=\\\\ =\sqrt[6]{(7\cdot2^2)^2\cdot(2\cdot7^2)^3}=\sqrt[6]{7^2\cdot2^4\cdot2^3\cdot7^6}=\\\\ =\sqrt[6]{49\cdot2^7\cdot7^6}=\sqrt[6]{49\cdot2\cdot2^6\cdot7^6}=2\cdot7\cdot\sqrt[6]{49\cdot2}=\\\\=\boxed{14\sqrt[6]{98}}=\\\\=14\sqrt[3]{\sqrt{2\cdot7^2}}=\boxed{14\sqrt[3]{7\sqrt{2}}}$