Question

Exercitiu scurt!! va rog <3​

Answer 1

Bună! ⚛

________

$\sqrt{2+\sqrt{2} } *\sqrt{2+\sqrt{2+\sqrt{2} } } *\sqrt{2-\sqrt{2+\sqrt{2} } } =$

$= \sqrt{(2+\sqrt{2} )*(2+\sqrt{2+\sqrt{2} })*(2-\sqrt{2+\sqrt{2} }) } =$

$= \sqrt{(2+\sqrt{2})*(2^{2} -\sqrt{2+\sqrt{2} }^{2} ) } =$

$=\sqrt{(2+\sqrt{2})*[4- (2+\sqrt{2})] } =$

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

$=\sqrt{(2+\sqrt{2})*(2-\sqrt{2} ) } =$

$=\sqrt{2^{2}-(\sqrt{2})^{2} } =$

$=\sqrt{4-2} =\sqrt{2}$