Question

Calcule as raízes por fatoração do radicando na imagem acima.

Answer 1

a)√49=7
b)√121=11
c)√169=13
d)√125=5
e)√625=5
f)√343=7
g)√81=3
h)√729=3
i)√128=2
j)√1024=2

desculpe n sei por raiz cúbica(ou mais) na resposta.

Answer 2

Olá, tudo bem?

Lembremos das seguintes propriedades de radiaciação e potenciação:

$\boxed{\sqrt[x]{a^x} =a}\ e\ \boxed{\sqrt[x]{a^x \cdot b} = a\sqrt[x]{b} }$

Vamos as respostas:



A)
49 / 7
7 / 7
1        => $7^2$

$\sqrt{49}= \sqrt{7^2}=\ \textgreater \ \boxed{7}$


B)
121 / 11
 11 / 11
 1            => $11^2$

$\sqrt{121}= \sqrt{11^2}=\ \textgreater \ \boxed{11}$


C)
169 / 13
 13 / 13
 1               => $13^2$

$\sqrt{169}= \sqrt{13^2}=\ \textgreater \ \boxed{13}$


D)
125 / 5
 25 / 5
 5 / 5    =>$5^3$

$\sqrt[3]{125}= \sqrt[3]{5^3}=\ \textgreater \ \boxed{5 }$


E)
625 / 5
125 / 5
 25 / 5
 5 / 5
1        => $5^4$

$\sqrt[4]{625}= \sqrt[4]{5^4}=\ \textgreater \ \boxed{5 }$



F)
343 / 7
  49 / 7
  7 / 7
 1           => $7^3$

$\sqrt[3]{343}= \sqrt[3]{7^3}=\ \textgreater \ \boxed{7}$



G)
81 / 3
27 / 3
9 / 3
3 / 3
1        => $3^4$

$\sqrt[4]{81}= \sqrt[4]{3^4}=\ \textgreater \ \boxed{3 }$


H)
729 / 3
243 / 3
 81 / 3
 27 / 3
  9 / 3
 3 / 3
 1         => $3^6$

$\sqrt[6]{729}= \sqrt[6]{3^6}=\ \textgreater \ \boxed{3}$


I)
128 / 2
 64 / 2
 32 / 2
 16 /2
  8 / 2
 4 / 2
 2 / 2
1          =>$2^7$

$\sqrt[7]{128} = \sqrt[7]{2^7}=\ \textgreater \ \boxed{2}$


J)
1024 / 2
 512 / 2
256 / 2
128 / 2
 64/ 2
32 / 2
16 / 2
 8 / 2
4 / 2
2 / 2
1         =>$2^{10}$

$\sqrt[10]{1024} = \sqrt[10]{2^{10}} =\ \textgreater \ \boxed{2}$