Question

ATIVIDADES 01. Usando a fatoração determine a raiz dos números abaixo: a) V1024 b) V162 343 d 3600 e) V225​

Answer 1

$\Large\boxed{\begin{array}{l}\tt a)\\\begin{array}{c|c}\sf1024&\sf2\\\sf512&\sf2\\\sf256&\sf2\\\sf128&\sf2\\\sf64&\sf2\\\sf32&\sf2\\\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}\\\sf 1024=2^{10}\\\sf\sqrt{1024}=\sqrt{2^{10}}=2^{10\div2}=2^5=32\blue{\checkmark}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt b)\\\begin{array}{c|c}\sf162&\sf2\\\sf81&\sf3\\\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 162=2\cdot 3^4\\\sf\sqrt{162}=\sqrt{2\cdot 3^4}\\\sf\sqrt{162}=\sqrt{2\cdot (3^2)^2}=3^2\sqrt{2}=9\sqrt{2}\blue{\checkmark}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt c)\\\begin{array}{c|c}\sf343&\sf7\\\sf49&\sf7\\\sf7&\sf7\\\sf1\end{array}\\\sf\sqrt[\sf3]{\sf343}=\sqrt[\sf3]{\sf 7^3}=7\blue{\checkmark}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt d)\\\begin{array}{c|c}\sf3600&\sf2\\\sf1800&\sf2\\\sf900&\sf2\\\sf450&\sf2\\\sf225&\sf3\\\sf75&\sf3\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf3600=(2^2)^2\cdot3^2\cdot 5^2\\\sf\sqrt{3600}=\sqrt{(2^2)^2\cdot3^2\cdot5^2}\\\sf\sqrt{3600}=2^2\cdot3\cdot5\\\sf\sqrt{3600}=4\cdot3\cdot5\\\sf\sqrt{3600}=60\blue{\checkmark}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt e)\\\begin{array}{c|c}\sf225&\sf3\\\sf75&\sf3\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 225=3^2\cdot5^2\\\sf\sqrt{225}=\sqrt{3^2\cdot5^2}\\\sf\sqrt{225}=3\cdot5\\\sf\sqrt{225}=15\blue{\checkmark}\end{array}}$