[tex]a) \ 1-\frac{1}{7}\cdot\sqrt{1\frac{27}{169}} =1-\frac{1}{7}\cdot\sqrt{\frac{1\cdot169+27}{169}} =1-\frac{1}{7}\cdot\sqrt\frac{196}{169}} =1-\frac{1}{7}\cdot\frac{14}{13} =1-\frac{7}{13} = \frac{6}{13}[/tex]
[tex]b) \ 16-16\cdot\sqrt{5\frac{1}{16}} = 16-16\cdot\sqrt{\frac{81}{16}} = 16-16\cdot\frac{9}{4} = 16-36 = -20[/tex]
[tex]c) \ 2+2\cdot\sqrt{1\frac{9}{16}} = 2+2\cdot\sqrt{\frac{25}{16}} = 2+2\cdot\frac{5}{4} = 2+\frac{5}{2} = 2+2\frac{1}{2} = 4\frac{1}{2}[/tex]
[tex]d) \ 4+\frac{1}{4}\cdot\sqrt{5\frac{11}{49}} =4+\frac{1}{4}\cdot\sqrt{\frac{256}{49}} = 4+\frac{1}{4}\cdot\frac{16}{7} = 4+\frac{4}{7} = 4\frac{4}{7}[/tex]
