Question

Factoriza u opera las siguientes expresiones radicales ​

Answer 1

Hola!

Explicación paso a paso:

a)

$\sqrt{ {3}^{4} {5}^{7} } = \sqrt{ {3}^{4} } \sqrt{ {5}^{7} } = {3}^{ \frac{4}{2} } \sqrt{ {5}^{7} } = {3}^{2} \sqrt{ {5}^{7} } = 9 \times \sqrt{ {5}^{7} }$

b)

$\sqrt{1200} = \sqrt{4 \times 300} \\ \\ = \sqrt{4 \times 4 \times 75} \\ \\ = \sqrt{4 \times 4 \times 25 \times 3} \\ \\ = \sqrt{ {4}^{2} \times {5}^{2} \times 3 } \\ \\ = \sqrt{ {4}^{2} } \times \sqrt{ {5}^{2} } \times \sqrt{3} \\ \\ = 4 \times 5 \times \sqrt{3} \\ \\ = 20 \sqrt{3}$

c)

$\sqrt[4]{ {6}^{7} {x}^{4} } = \sqrt[4]{ {x}^{4} {6}^{7} } = \sqrt[4]{ {x}^{4} } \sqrt[4]{ {6}^{7} } = x \sqrt[4]{ {6}^{7} }$

d)

$\sqrt[4]{128} = \sqrt[4]{2 \times 64} \\ = \sqrt[4]{2 \times 2\times 32} \\ = \sqrt[4]{2 \times 2 \times 2 \times 16} \\ = \sqrt[4]{2 \times 2 \times 2 \times 2 \times 8} \\ = \sqrt[4]{ {2}^{4} \times {2}^{3} } \\ = \sqrt[4]{ {2}^{4} } \times \sqrt[4]{ {2}^{3} } \\ = 2 \sqrt[4]{ {2}^{3} }$

e)

$\sqrt[3]{81 {x}^{4} } \\ = \sqrt[3]{ {3}^{3} \times 3 \times {x}^{4} } \\ = \sqrt[3]{ {3}^{3} } \times \sqrt[3]{3 \times {x}^{4} } \\ = 3 \times \sqrt[3]{3 {x}^{4} } \\ = 3 \sqrt[3]{3 {x}^{4} }$