Question

O valor de $\sqrt{19-6 \sqrt{2} }$ é?

Answer 1

$\mathrm{Note\ que\ \big(19-6\sqrt{2}\big)\ pode\ ser\ escrito\ como}\\ \mathrm{um\ produto\ not\'avel:}\\\\ \mathrm{19-6\sqrt{2}=18-2.3\sqrt{2}+1=(3\sqrt{2})^2+2.3\sqrt{2}.(-1)+(-1)^2}\\ \mathrm{19-6\sqrt{2}=\big(3\sqrt{2}-1\big)^2}\\\\ \mathrm{Portanto:}\\\\ \mathrm{\sqrt{\big(19-6\sqrt{2}\big)}=\sqrt{\big(3\sqrt{2}-1\big)^2}=\boxed{\mathbf{3\sqrt{2}-1}}}$