$a)$

${11}^2=121{13}^2=169{15}^2=225{17}^2=289{19}^2=361$

${12}^2=144{14}^2=196{16}^2=256{18}^2=324{20}^2=400$

$b)$

$\sqrt{\frac{144}{121}}=\sqrt{{\left(\frac{12}{11}\right)}^2}=\frac{12}{11}$

$\sqrt{\frac{324}{289}}=\sqrt{{\left(\frac{18}{17}\right)}^2}=\frac{18}{17}=1\frac{1}{17}$

$\sqrt{\frac{225}{361}}=\sqrt{{\left(\frac{15}{19}\right)}^2}=\frac{15}{19}$

$\sqrt{\frac{169}{196}}=\sqrt{{\left(\frac{13}{14}\right)}^2}=\frac{13}{14}$

$\sqrt{2\frac{1}{144}}=\sqrt{\frac{289}{144}}=\sqrt{{\left(\frac{17}{12}\right)}^2}=\frac{17}{12}=1\frac{5}{12}$

$\sqrt{1\frac{48}{121}}=\sqrt{\frac{169}{121}}=\sqrt{{\left(\frac{13}{11}\right)}^2}=\frac{13}{11}=1\frac{2}{11}$