Question

Decomponha o radicando em fatores primos e calcule as raízes:
√625 =

⁴√81 =

³√27/1000

ME AJUDEEMM PFV PRECISO PRA AGORA

Answer 1

1) √625

625 (por 5)

125 (por 5)

25 (por 5)

5 (por 5)

1

√5⁴

5^2

25

2) ⁴√81

81 (por 3)

27 (por 3)

9 (por 3)

3 (por 3)

1

⁴√3⁴

3

3) ³√27/1000

³√3³/10³

3/10

Answer 2

Olá,

a)

$\sf \: \sqrt{625}$

625 | 5

125 | 5

25 | 5

5 | 5

1

$\sf \: 625 = 5. \: 5. \: 5. \: 5 \: = {5}^{2} . \: {5}^{2} \\ \\ \sf \: \sqrt{625} = \sqrt{ {5}^{2}. \: {5}^{2} } = 5. \: 5 = \boxed{ \sf \: 25}$

b)

$\sf \: \sqrt[4]{81}$

81 | 3

27 | 3

9 | 3

3 | 3

1

$\sf \: 81 = 3. \: 3. \: 3. \: 3 = {3}^{4} \\ \\ \sf \: \sqrt[4]{81} = \sqrt[4]{ {3}^{4} } = \sqrt[ \cancel{4}]{ {3}^{ \cancel{4}} } = \: \boxed{ \sf \: 3}$

c)

$\sf \: \sqrt[3]{ \frac{27}{1000} } = \frac{ \sqrt[3]{27} }{ \sqrt[3]{1000} }$

27 | 3

9 | 3

3 | 3

1

$\sf \: 27 = 3. \: 3. \: 3 = {3}^{3} \\ \\ \sf \: \sqrt[3]{27} = \sqrt[3]{ {3}^{3} } = \sqrt[ \cancel{3}]{ {3}^{ \cancel{3} }} = \boxed{ \sf \: 3}$

1000 | 2

500 | 2

250 | 2

125 | 5

25 | 5

5 | 5

1

$\sf \: 1000 = 2. \: 2. \: 2. \: 5. \: 5. \: 5 = {2}^{3} . \: {5}^{3} \\ \\ \sf \: \sqrt[3]{1000} = \sqrt[3]{ {2}^{3}. \: {5}^{3} } = \sqrt[ \cancel{3}]{ {2}^{ \cancel{3}} . \: {5}^{ \cancel{3}} } = 2. \: 5 = \boxed{ \sf \: 10}$

$\sf \: \sqrt[3]{ \frac{27}{1000} } = \boxed{\sf \: \frac{3}{10}}$