Question

Simplifique as expressões raiz quadrada de 396 menos raiz quadrada de 108 mais raiz quadrada de 176 mais raiz quadrada de 675

Answer 1

$\sqrt{396} - \sqrt{108} + \sqrt{176} + \sqrt{675} = \\ \\ fatora \\ \\ \sqrt{2^2.3^2.11} - \sqrt{2^2.3^2.3} + \sqrt{2^2.2^2.11} + \sqrt{3^2.3.5^2} = \\ \\ 2.3 \sqrt{11} -2.3 \sqrt{3} +2.2 \sqrt{11} +3.5 \sqrt{3} = \\ \\ 6 \sqrt{11} -6 \sqrt{3} +4 \sqrt{11} +15 \sqrt{3} = \\ \\ 6 \sqrt{11} +4 \sqrt{11} -6 \sqrt{3} +15 \sqrt{3} = \\ \\ 10 \sqrt{11} +9 \sqrt{3}$ 

fatoração

$396|2~~~~~~108|2~~~~~~176|2~~~~~~675|3 \\ 198|2~~~~~~~54|2~~~~~~~~88|2~~~~~~225|3 \\ ~~99|3~~~~~~~~27|3~~~~~~~44|2~~~~~~~~75|3 \\ ~~33|3~~~~~~~~~9|3~~~~~~~~22|2~~~~~~~~25|5 \\ ~~11|11~~~~~~~~3|3~~~~~~~11|11~~~~~~~~5|5 \\ ~~~1~~~~~~~~~~~~1~~~~~~~~~~~1~~~~~~~~~~~~1$