Question

extrair as raízes por decomposição;

A)
B)
C)
D)
E)
F)
G)
H)
I)​

Answer 1

A)

$4 \sqrt{108} = \\ 108 | 2 \\ 54 |2 \\ 27 | 3 \\ 9 | 3 \\ 3 | 3 \\ 1......... \\ \sqrt{ {2}^{2} \times {3}^{2} \times 3 } = 2 \times 3 \sqrt{3} = 6 \sqrt{3} \\ \\ 4 \times 6 \sqrt{3} = 24 \sqrt{3}$

B)

$\sqrt[3]{216} = \\ 216 | 2 \\ 108 | 2 \\ 54 | 2 \\ 27 |3 \\ 9 | 3 \\ 3 | 3 \\ 1 | .......... \\ \sqrt{ {2}^{2} \times 2 \times {3}^{2} \times 3 } = 2 \times 3 \sqrt{2 \times 3} \\ \\ 6 \sqrt{6}$

C)

$2 \sqrt[2]{54} \\ 54 | 2 \\ 27 | 3 \\ 9 | 3 \\ 3 | 3 \\ 1 | ............ \\ \sqrt{2 \times {3}^{2} \times 3 } = 3 \sqrt{2 \times 3} = 3 \sqrt{6} \\ \\ 2 \times 3 \sqrt{6} = 6 \sqrt{6}$

D)

$\sqrt{96} = \\ \\ 96 | 2 \\ 48 |2 \\ 24 | 2 \\ 12 | 2 \\ 6 | 2 \\ 3 | 3 \\ 1 | .......... \\ \sqrt{ {2}^{2} \times {2}^{2} \times 2 \times 3} = 2 \times 2 \sqrt{6} = 4 \sqrt{6}$

E)

$\sqrt{60} = \\60 | 2 \\ 30 | 2 \\ 15 | 3 \\ 5 | 5 \\ 1 | ............ \\ \sqrt{ {2}^{2} \times 3 \times 5} = 2 \sqrt{15}$

F)

$- 5 \sqrt{48} = \\ \\ 48 | 2 \\ 24 | 2 \\ 12 | 2 \\ 6 | 2 \\ 3 | 3 \\ 1 | ........ \\ \sqrt{ {2}^{2} \times {2}^{2} \times 3 } = 2 \times 2 \sqrt{3} = 4 \sqrt{3} \\ \\ - 5 + 4 \sqrt{3} = - \sqrt{3}$

G)

$\sqrt{192} \\ \\ 192 | 2 \\ 96 | 2 \\ 48 | 2 \\ 24| 2 \\ 12 | 2 \\ 6 | 2 \\ 3 | 3 \\ 1 | ............. \\ \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} \times 3 } = \\ \\ 2 \times 2 \times 2 \sqrt{3} = 8 \sqrt{3}$

H)

$2 \sqrt{243} = \\ 243 | 3 \\ 81 | 3 \\ 27 | 3 \\ 9 | 3 \\ 3 | 3 \\ 1 | .......... \\ \sqrt{ {3}^{2} \times {3}^{2} \times 3 } = 3 \times 3 \sqrt{3} = 9 \sqrt{3} \\ \\ 2 \times 9 \sqrt{3} = 18 \sqrt{3}$

I)

$\sqrt[3]{80} = \\ 80 | 2 \\ 40 | 2 \\ 20 | 2 \\ 10 | 2 \\ 5 | 5 \\ 1 | ..... \\ \sqrt{ {2}^{3} \times 2 \times 5} = 2 \sqrt[3]{2 \times 5} = 2 \sqrt[3]{10}$

J)

$- 3 \sqrt{121} = \\ 121 | 11 \\ 11 | 11 \\ 1 | .......... \\ {11}^{2} \\ \\ \sqrt{ {11}^{2} } = 11 \\ \\ - 3 + 11 = 8$