Question

Qual é o valor da expressão: √∛4096 +3√√1296 -√√√6561

Answer 1

$\sqrt{ \sqrt[3]{4096} } +3 \sqrt{ \sqrt{1296} } - \sqrt{ \sqrt{ \sqrt{6561} } } =$ 

multiplica os índices reduzindo a um só radical

$\sqrt[6]{4096} +3 \sqrt[4]{1296} - \sqrt[8]{6561} =$ 

fatora , tirando do radical os algarismos de expoentes iguais ao índice

$\sqrt[6]{2^6.2^6} +3. \sqrt[4]{2^4.3^4} - \sqrt[8]{3^8} = \\ \\ 2.2+3.2.3-3= \\ \\ 4+18-3= \\ \\ 22-3=19$ 

fatoração

$4096|2~~~~~~~~~~1296|2~~~~~~~~~~6561|3 \\ 2048|2~~~~~~~~~~~648|2~~~~~~~~~~~2187|3 \\ 1024|2~~~~~~~~~~~324|2~~~~~~~~~~~~~729|3 \\ ~~512~|2~~~~~~~~~~162|2~~~~~~~~~~~~~~243|3 \\ ~~256~|2~~~~~~~~~~~~81|3~~~~~~~~~~~~~~~81|3 \\ ~~128~|2~~~~~~~~~~~~27|3~~~~~~~~~~~~~~~27|3 \\ ~~~64~|2~~~~~~~~~~~~~9~|3~~~~~~~~~~~~~~~~9|3 \\ ~~~32~|2~~~~~~~~~~~~~3~|3~~~~~~~~~~~~~~~~3|3 \\ ~~~16~|2~~~~~~~~~~~~~1~~~~~~~~~~~~~~~~~~~~1 \\ ~~~~~8|2 \\ ~~~~~4|2 \\ ~~~~~2|2 \\ ~~~~~1$