Question

Qual a raiz quadrada de 2,56 fatoração?

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Propriedade\,do\,radical\,aritm\acute etico}\\\huge\boxed{\boxed{\boxed{\boxed{\sf \sqrt[\sf n]{\sf a^n}=a}}}}\end{array}}$

$\Large\boxed{\begin{array}{l}\begin{array}{c|c}\sf256&\sf2\\\sf128&\sf2\\\sf64&\sf2\\\sf32&\sf2\\\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}\\\sf 256=2^2\cdot2^2\cdot2^2\cdot2^2\\\begin{array}{c|c}\sf100&\sf2\\\sf50&\sf2\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 100=2^2\cdot5^2\\\sf \sqrt{2,56}=\sqrt{\dfrac{256}{100}}\\\\\sf \sqrt{2,56}=\sqrt{\dfrac{\diagup\!\!\!\!\!2^2\cdot2^2\cdot2^2\cdot2^2}{\diagup\!\!\!\!2^2\cdot5^2}}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf \sqrt{2,56}=\sqrt{\dfrac{2^2\cdot2^2\cdot2^2}{5^2}}\\\\\sf\sqrt{2,56}=\dfrac{2\cdot2\cdot2}{5}\\\\\sf\sqrt{2,56}=\dfrac{8}{5}\\\\\sf\sqrt{2,56}=1,6\end{array}}$