$\dfrac{2+\sqrt{2}}{\sqrt{1,5+\sqrt{2}}}$
$=\dfrac{2(2+\sqrt{2})}{2(\sqrt{1,5+\sqrt{2}})}$
$=\dfrac{2(2+\sqrt{2})}{\sqrt{4(1,5+\sqrt{2})}}$
$=\dfrac{2(2+\sqrt{2})}{\sqrt{6+4\sqrt{2}}}$
$=\dfrac{2(2+\sqrt{2})}{\sqrt{4+2.2.\sqrt{2}+2}}$
$=\dfrac{2(2+\sqrt{2})}{\sqrt{(2+\sqrt{2})^{2}}}$
$=\dfrac{2(2+\sqrt{2})}{2+\sqrt{2}}$
$=2$