[tex](\sqrt{2}-1)*\sqrt{3+\sqrt{8}}=\\=(\sqrt{2}-1)*\sqrt{3+2\sqrt{2}}=\\=(\sqrt{2}-1)*\sqrt{(\sqrt{2}+1)^{2}}=\\=(\sqrt{2}-1)*(\sqrt{2}+1)=\\=\sqrt{2}^{2}-1^{2}=2-1=1.[/tex]
/rfd
