Question

Calcule,indicando o resultado sem radical.

Answer 1

Resposta:

a) 6

b) 2

c) 2

d) 11

e) 10

f) 2

g) 1

h) 5

Explicação passo-a-passo:

a)

$\sqrt{3}\cdot\sqrt{12} = \sqrt{3}\cdot\sqrt{3\cdot4}\\\sqrt{3}\cdot\sqrt{3}\cdot\sqrt{4}\\\sqrt{3^2}\cdot\sqrt{4}= \sqrt{9}\cdot\sqrt{4} = 3\cdot2=6$

b)

$\sqrt[3]{2} \cdot \sqrt[3]{4} = \sqrt[3]{2\cdot4}=\sqrt[3]{8}\\2^3 = 8\therefore\sqrt[3]{8}=2$

c)

$\sqrt[5]{8}\cdot\sqrt[5]{4}=\sqrt[5]{8\cdot4}\\\sqrt[5]{8\cdot4} = \sqrt[5]{32}\\2^5 = 32 \therefore \sqrt[5]{32} = 2$

d)

$\sqrt{11}\cdot\sqrt{11} = \sqrt{11\cdot11} = \sqrt{11^2} = 11$

e)

$\sqrt{2}\cdot\sqrt{50} = \sqrt{2\cdot50}\\\sqrt{2\cdot50} = \sqrt{2\cdot2\cdot25}\\\sqrt{2\cdot2\cdot25} = \sqrt{2^2\cdot25}\\\sqrt{2^2\cdot25} = 2\sqrt{25} = 2\cdot5=10$

f)

$\sqrt{8}\cdot\sqrt{0.5} = \sqrt{8\cdot\frac{1}{2}}\\\sqrt{8\cdot\frac{1}{2}} = \sqrt{\frac{8}{2}} = \sqrt{4} = 2$

g)

$\sqrt{0.1}\cdot\sqrt{10} = \sqrt{\frac{1}{10}\cdot10}\\\sqrt{\frac{1}{10}\cdot10}=\sqrt{\frac{10}{10}} = \sqrt{1}=1$

h)

$\sqrt{0.5}\cdot\sqrt{5}\cdot\sqrt{10} = \sqrt{\frac{1}{2}\cdot5\cdot10}\\\sqrt{\frac{1}{2}\cdot50}=\sqrt{\frac{50}{2}}=\sqrt{25}=5$