Question

Raiz de 2 + 2 sobre raiz de 2

Answer 1

$\sqrt{2} + \frac{ 2}{ \sqrt{2} }$


mmc de √2 e 1 = √2

$\frac{ \sqrt{2}. \sqrt{2} }{ \sqrt{2} } + \frac{2}{ \sqrt{2} }$


$\frac{ \sqrt{4} }{ \sqrt{2} } + \frac{2}{ \sqrt{2} }$

$\frac{2}{ \sqrt{2} } + \frac{2}{ \sqrt{2} } = \frac{4}{ \sqrt{2} }$

(multiplico ambos por √2)

$\frac{4}{ \sqrt{2} } . \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{4 \sqrt{2} }{ \sqrt{4} } = \frac{4 \sqrt{2} }{2} =\boxed{2 \sqrt{2} }\ \ \ \ \ \ \ ok$

Answer 2

$\displaystyle \frac{\sqrt{2}+2}{\sqrt{2}}=\frac{\sqrt2+2}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{(\sqrt2+2)(\sqrt2)}{\sqrt2\cdot\sqrt2}=\frac{2+2\sqrt2}{2}=\boxed{1+\sqrt2}$
Considerando: $\sqrt2\approx1,41$
$\displaystyle 1+\sqrt2\approx1+1,41\approx2,41\Longleftrightarrow \frac{2+\sqrt2}{\sqrt2}\approx\frac{2+1,41}{1,41}\approx \frac{3,41}{1,41}\approx\boxed{2,41}$