Question

2°)Determine a raiz quadrada exata dos números a seguir:

a)2304
b)676
c)2500
d)1764​

Quero cálculo​

Answer 1

$\Large\boxed{\begin{array}{l}\rm a)\\\begin{array}{c|c}\sf2304&\sf2\\\sf1152&\sf2\\\sf576&\sf2\\\sf288&\sf2\\\sf144&\sf2\\\sf72&\sf2\\\sf36&\sf2\\\sf18&\sf2\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 2304=2^2\cdot2^2\cdot2^2\cdot2^2\cdot3^2\\\sf \sqrt{2304}=\sqrt{2^2\cdot2^2\cdot2^2\cdot2^2\cdot3^2}\\\sf\sqrt{2304}=2\cdot2\cdot2\cdot2\cdot3\\\sf\sqrt{2304}=48\end{array}}$

$\Large\boxed{\begin{array}{l}\rm b)\\\begin{array}{c|c}\sf676&\sf2\\\sf338&\sf2\\\sf169&\sf13\\\sf13&\sf13\\\sf1\end{array}\\\sf 676=2^2\cdot13^2\\\sf\sqrt{676}=\sqrt{2^2\cdot13^2}\\\sf\sqrt{676}=2\cdot13\\\sf\sqrt{676}=26\\\sf\end{array}}$

$\Large\boxed{\begin{array}{l}\rm c)\\\begin{array}{c|c}\sf2500&\sf2\\\sf1250&\sf2\\\sf625&\sf5\\\sf125&\sf5\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 2500=2^2\cdot5^2\cdot5^2\\\sf \sqrt{2500}=\sqrt{2^2\cdot5^2\cdot5^2}\\\sf\sqrt{2500}=2\cdot5\cdot5\\\sf\sqrt{2500}=50\end{array}}$

$\Large\boxed{\begin{array}{l}\rm d)\\\begin{array}{c|c}\sf1764&\sf2\\\sf882&\sf2\\\sf441&\sf3\\\sf147&\sf3\\\sf49&\sf7\\\sf7&\sf7\\\sf1\end{array}\\\sf 1764=2^2\cdot3^2\cdot7^2\\\sf\sqrt{1764}=\sqrt{2^2\cdot3^2\cdot7^2}\\\sf\sqrt{1764}=2\cdot3\cdot7\\\sf \sqrt{1764}=42\end{array}}$