[tex]\sqrt{1\frac{11}{25} } *\sqrt{1\frac{9}{16} } -{(\sqrt{{6\frac{1}{4}}}- \sqrt{1\frac{13}{36} } } ):\sqrt{1\frac{7}{9} }=\\\\=\sqrt{\frac{36}{25} } *\sqrt{\frac{25}{16} } -{(\sqrt{{6\frac{1}{4}}}- \sqrt{1\frac{13}{36} } } )^2:\sqrt{1\frac{7}{9} }=\\\\=\frac{6}{5} *\frac{5}{4} -{(\sqrt{{6\frac{1}{4}}}- \sqrt{1\frac{13}{36} } } )^2:\sqrt{1\frac{7}{9} }=\\\\=\frac{3}{2} -{(\sqrt{{\frac{25}{4}}}- \sqrt{\frac{49}{36} } } )^2:\sqrt{\frac{16}{9} }=\\\\[/tex]
[tex]\\=\frac{3}{2} -(\frac{5}{2}-\frac{7}{6} )^2:\frac{4}{3} =\\\\=\frac{3}{2}-(\frac{15}{6} -\frac{7}{6} )^2*\frac{3}{4} =\\\\=\frac{3}{2} -(\frac{4}{3} )^2*\frac{3}{4} =\\\\=\frac{3}{2} -\frac{16}{9} *\frac{3}{4} =\\\\=\frac{3}{2} -\frac{4}{3} =\\\\=\frac{9}{6} -\frac{8}{6}\\\\=\frac{1}{6}[/tex]
