Question

Calcule através de fatoração:

Answer 1

a)

$\sqrt{900} = \sqrt{ {2}^{2} \times {3}^{2} \times {5}^{2} } = 2 \times 3 \times 5 = 30$

b)

$\sqrt[3]{8} = \sqrt[3]{ {2}^{3} } = 2$

c)

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

d)

$\sqrt{1024} = \sqrt{ {2}^{10} } = {2}^{ \frac{10}{2} } = {2}^{5} = 32$

e)

$\sqrt[3]{ \frac{8}{64} } = \frac{ \sqrt[3]{8} }{ \sqrt[3]{64} } = \frac{ \sqrt[3]{ {2}^{3} } }{ \sqrt[3]{ {2}^{6} } } = \frac{2}{ {2}^{ \frac{6}{3} } } = \frac{2}{ {2}^{2} } = \frac{2}{4} = \frac{1}{2}$

f)

$\sqrt[3]{512} = \sqrt[3]{ {2}^{9} } = {2}^{\frac{9}{3} } = {2}^{3} = 8$