Question

efetue as multiplicações ​

Answer 1

Resposta:

$\sqrt{2}(5\sqrt{2}-10\sqrt{8})\\=2(5.2-10\sqrt{4.2} \\=10.2^{2} -20.2\sqrt{2}\\=10.4-40\sqrt{2} \\=40-40\sqrt{2} \\=\sqrt{2}$

Explicação passo-a-passo:

Answer 2

Resposta:

Segue o passo a passo

Explicação passo-a-passo:

3) a)

$\sqrt{2} (5\sqrt{2}-10\sqrt{8})=\\\sqrt{2}(5\sqrt{2}-10\sqrt{2^{3} } )=\\\sqrt{2}(5\sqrt{2}-10.2\sqrt{2} )=\\\sqrt{2}(5\sqrt{2}-20\sqrt{2} )=\\\sqrt{2}(-15\sqrt{2})=\\-15\sqrt{2}.\sqrt{2}= \\ -15.2=\\-30$

b)

$\sqrt{5}(8+\sqrt{5}-\sqrt{20} ) = \\\sqrt{5}(8+\sqrt{5}-\sqrt{4.5} ) = \\\sqrt{5}(8+\sqrt{5}-2\sqrt{5} ) = \\\sqrt{5}(8-\sqrt{5} ) = \\8\sqrt{5}-\sqrt{5}.\sqrt{5}  = \\8\sqrt{5} -5$

c)

$\sqrt{7+\sqrt{13} } .\sqrt{7-\sqrt{13} }=\\\sqrt{(7+\sqrt{13}).(7-\sqrt{13})} =\\\sqrt{7^{2}- \sqrt{13}^{2}}} = \\\sqrt{49-13} =\\\sqrt{36} =\\6$

d)

$(\frac{\sqrt{6} + \sqrt{2}  }{2})^2 =\\(\frac{\sqrt{6} }{2} +\frac{\sqrt{2} }{2})^2 =\\(\frac{6}{4}+2. \frac{\sqrt{6} }{2}.\frac{\sqrt{2} }{2}+\frac{2}{4} )=\\\frac{3}{2}+\frac{2\sqrt{12} }{4} +\frac{1}{2} =\\ \frac{4}{2} +\frac{2.2\sqrt{3} }{4} =\\2+\frac{4\sqrt{3} }{4} =\\2+\sqrt{3}$