Question

Conseguem resolver pra mim?
Não liguem pras respostas (a foto é de um amigo meu)​

Answer 1

1) a)

$\sqrt{12} = \sqrt{ {2}^{2} .3} = 2 \sqrt{ 3}$

b)

$\sqrt{20} = \sqrt{ {2}^{2} .5} = 2 \sqrt{5}$

c)

$\sqrt{50} = \sqrt{2. {5}^{2} } = 5 \sqrt{2}$

d)

$\sqrt{243} = \sqrt{ {3}^{4} .3 } = 9 \sqrt{3}$

e)

$\sqrt[3]{625} = \sqrt[3]{ {5}^{3} .5} = 5 \sqrt[3]{5}$

f)

$\sqrt[4]{2048} = \sqrt[4]{ {2}^{8}. {2}^{3} } = 4 \sqrt[4]{8}$

2)

a)

$3 \sqrt{5} + \sqrt{5} - 6 \sqrt{5} = - 2\sqrt{5}$

b)

$5 \sqrt[3]{3} + 2 \sqrt[3]{3} - 2 \sqrt[3]{3} + \sqrt[3]{3} \\ = 6 \sqrt[3]{3}$

c)

$- 4 + \sqrt[3]{5} + 2 \sqrt[3]{5} - 4 \\ = - 8 + 3 \sqrt[3]{5}$

d)

$2 \sqrt[3]{3} - 2 \sqrt{3} + 3 \sqrt{3} + 3 \sqrt[3]{3} \\ = 5 \sqrt[3]{3} + \sqrt{3}$

3)

a)

$3 \sqrt[4]{2} . \sqrt[4]{8} = 3 \sqrt[4]{16} = 3.2 = 6$

b)

$\sqrt{2} . \sqrt{6} . \sqrt{3} = \sqrt{36} = 6$

c)

$\sqrt{2} . \sqrt{8} = \sqrt{16} = 4$

d)

$\sqrt[3]{4} . \sqrt[3]{6} = \sqrt[3]{24} \\ = \sqrt[3]{ {2}^{3} .3} = 2 \sqrt[3]{3}$

4)

a)

$\sqrt[3]{20} \div \sqrt[3]{10} = \sqrt[3]{2}$

b)

$\sqrt{28} \div \sqrt{7} = \sqrt{4 } = 2$

c)

$30 \sqrt{15} \div 5 \sqrt{3} = 6 \sqrt{5}$

d)

$\sqrt{50} \div \sqrt{2} = \sqrt{25} = 5$

5)

a)

$\sqrt{ \sqrt{10} } = \sqrt[4]{10}$

b)

$\sqrt[3]{ \sqrt{3} } = \sqrt[6]{3}$c)

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

d)

$\sqrt[3]{ \sqrt[3]{ \sqrt{3} } } = \sqrt[18]{3}$

6)

a)

$\sqrt{ {8}^{2} } = 8$

b)

$\sqrt[3]{ {7}^{3} } = 7$

c)

$\sqrt[5]{ {x}^{5} } = x$

d)

$\sqrt{ {(7a)}^{2} } = 7a$

7)

a)

$\sqrt{5} . \sqrt{7} = \sqrt{5.7} = \sqrt{35}$

b)

$\sqrt[3]{5.x} = \sqrt[3]{5} . \sqrt[3]{x}$

c)

$\sqrt[3]{2} . \sqrt[3]{8} = \sqrt[3]{2.8} = \sqrt[3]{16}$

d)

$\sqrt{10x} . \sqrt{y} = \sqrt{10xy}$