Question

Simplifique as seguintes expressões quando for possível:

a)√9000
b)⁴√7⁵.7³
c)¹⁰√2¹⁵. 3⁸

Answer 1

$a) \sqrt{9000}= \sqrt{9.1000} = \sqrt{3^{2}.10^{3}} =\sqrt{3^{2}.10^{2}.10^{1}} = 3.10. \sqrt{10} \\ \\ b) \sqrt[4]{7^{5}.7^{3}} = \sqrt[4]{7^{8}} = 7^{2} = 49 \\ \\ c) \sqrt[10]{2^{15}.3^{8}} = \sqrt[10]{2^{15}}. \sqrt[10]{3^{8}} = \sqrt[10]{2^{10}.2^{5}}. \sqrt[10]{3^{8}}=2. \sqrt[10]{2^{5}}. \sqrt[5]{3^{4}} \\ 2. \sqrt{2}. \sqrt[5]{3^{4}}$


Espero ter ajudado.