Question

Efetue: √2·√(2+√2)·√[2+√(2+√2)]·√[2-√(2+√2)]

Answer 1

chamando $\sqrt{2+ \sqrt{2}} = x$, temos a equaçao:

$\sqrt{2} \times x \times \sqrt{2 + x} \times \sqrt{2 - x} = \\ \sqrt{2} \times x \times \sqrt{(2 + x)(2 - x)} = \\ \sqrt{2} \times x \times \sqrt{4 - {x}^{2} } \\ x \sqrt{8 - 2 {x}^{2} }$

agora voltando com o valor de x:

$\sqrt{2 + \sqrt{2} }\sqrt{8 - 2(2 + \sqrt{2}) } = \\ \sqrt{2 + \sqrt{2} } \sqrt{4 - 2 \sqrt{2} } = \\ \sqrt{2(2 + \sqrt{2} )(2 - \sqrt{2}) } = \\ \sqrt{2(4 - 2)} = \\ \sqrt{4} = \\ 2$

Answer 2

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