Question

Determine o valor da expressão
      $\sqrt[6]{729}$ +$\sqrt[5]{1024}$-$\sqrt[3]{125}$

Answer 1

Fatorando cada um:

$729 \ | \ 3 \\ 243 \ | \ 3 \\ 81 \ \ \ | \ 3 \\ 27 \ \ \ | \ 3 \\ 9 \ \ \ \ | \ 3 \\ 3 \ \ \ \ | \ 3 \\ 1 \\\\ \sqrt[6]{729} = \sqrt[6]{3^{6}} = \boxed{3}$


$1024 \ | \ 4 \\ 256 \ \ | \ 4 \\ 64 \ \ \ \ | \ 4 \\ 16 \ \ \ \ | \ 4 \\ 4 \ \ \ \ \ | \ 4 \\\\ \sqrt[5]{1024} = \sqrt[5]{4^{5}} = \boxed{4}$


$125 \ | \ 5 \\ 25 \ \ | \ 5 \\ 5 \ \ \ \ | \ 5 \\ 1 \\\\ \sqrt[3]{125} = \sqrt[5]{5^{3}} = \boxed{5}$



$\sqrt[6]{729} + \sqrt[5]{1024} - \sqrt[3]{125} = 3+4-5 = \boxed{\boxed{\boxed{2}}}$