Question

efetue as operações

Answer 1

Olá, tudo bem?

Em cada caso, sempre que possível, devemos decompor em números primos e fatorar o radicando:

Vamos lá:

A)
 
27 / 3
  9/ 3
3 / 3
1         =>3².3

$\sqrt{3}+\sqrt{27}=\sqrt{3}+\sqrt{3^2\cdot3}=\sqrt{3}+3\sqrt{3}=\\1+3\sqrt{3}=\ \textgreater \ \boxed{\boxed{4\sqrt{3}}}$


B)
75 / 3                        12 / 2
25 / 5                         6 / 2
5 / 5                          3 / 3
1      =>5².3               1       =>2².3

$\sqrt{75}-\sqrt{12}=\sqrt{5^2\cdot3}-\sqrt{2^2\cdot3}=\\5\sqrt{3}-2\sqrt{3}=\\5-2\sqrt{3}=\ \textgreater \ \boxed{\boxed{3\sqrt{3}}}$


C)
50 / 2
25 / 5
 5 / 5
1        =>5².2

$7\sqrt{2}+\sqrt{50}=7\sqrt{2}+\sqrt{5^2\cdot2}=\\ 7\sqrt{2}+5\sqrt{2}=7+5\sqrt{2}=\\ \boxed{\boxed{12\sqrt{2}}}$


D)
$\sqrt{12}=2\sqrt{3}\ (Veja\ letra\ B)\\\\ \sqrt{75}=5\sqrt{3}\ (Veja\ letra\ B)\\\\\\ \sqrt{12} - \sqrt{75} + \sqrt{3}=\\ 2\sqrt{3}-5\sqrt{3}+1\sqrt{3}=\\ 2-5 +1\sqrt{3}=\boxed{\boxed{-(3\sqrt{3})}}$


E)

20 / 2
10 / 2
5 /5
1          => 2².5


32 / 2
16 / 2
 8 / 2
4 / 2
2 / 2
1     => 2².2².2

45 / 3
15 / 3
5 / 5
1      =>3².5

$\sqrt{50}=5\sqrt{2}\ (Veja\ letra\ C)$

$3\sqrt{20}+\sqrt{32}-2\sqrt{45}+\sqrt{50}=\\ 3\cdot2\sqrt{5}+4\sqrt{2}-2\cdot3\sqrt{5}+5\sqrt{2}=\\ 6\sqrt{5}+4\sqrt{2}-6\sqrt{5}+5\sqrt{2}=\\ 6\sqrt{5}-6\sqrt{5}+4\sqrt{2}+5\sqrt{2}=\\ 4+5\sqrt{2}=\\\\ \boxed{\boxed{9\sqrt{2}}}$


F)
125 / 5
 25 / 5
 5 /5
1               =>5².5

$\sqrt{27}=3\sqrt{3}\ (Letra\ A)\\\\ \sqrt{20}=2\sqrt{5}\ (Letra\ E)\\\\ \sqrt{12}=2\sqrt{3}\ (Letra\ B)\\\\\\ \sqrt{125}+2\sqrt{27}-\sqrt{20}+3\sqrt{12}=\\ \sqrt{5^2\cdot5}+2\cdot3\sqrt{3}-2\sqrt{5}+3\cdot2\sqrt{3}=\\ 5\sqrt{5}+6\sqrt{3}-2\sqrt{5}+6\sqrt{3}=\\ 5\sqrt{5}-2\sqrt{5}+6\sqrt{3}+6\sqrt{3}=\\ 5-2\sqrt{5}+(6+6)\sqrt{3}=\\\\ \boxed{\boxed{3\sqrt{5}+12\sqrt{3}}}$


Acho que é isso.
Espero ter ajudado.
Bons estudos!