$\text{a)}\sqrt{2\frac{7}{9}}=\sqrt{\frac{25}{9}}=\frac{\sqrt{25}}{\sqrt{9}}=\frac{5}{3}=1\frac{2}{3}$  

---

$\text{b)}\sqrt{1\frac{9}{16}}=\sqrt{\frac{25}{16}}=\frac{\sqrt{25}}{\sqrt{16}}=\frac{5}{4}=1\frac{1}{4}$  

---

$\text{c)}\sqrt{1\frac{7}{9}}=\sqrt{\frac{16}{9}}=\frac{\sqrt{16}}{\sqrt{9}}=\frac{4}{3}=1\frac{1}{3}$  

---

$\text{d)}\sqrt{5\frac{1}{16}}=\sqrt{\frac{81}{16}}=\frac{\sqrt{81}}{\sqrt{16}}=\frac{9}{4}=2\frac{1}{4}$  

---

$\text{e)}\sqrt{5\frac{4}{9}}=\sqrt{\frac{49}{9}}=\frac{\sqrt{49}}{\sqrt{9}}=\frac{7}{3}=2\frac{1}{3}$  

---

$\text{f)}\sqrt{1\frac{81}{19}}=\sqrt{\frac{100}{81}}=\frac{\sqrt{100}}{\sqrt{81}}=\frac{10}{9}=1\frac{1}{9}$  

---

$\text{g)}\sqrt{18\frac{7}{9}}=\sqrt{\frac{169}{9}}=\frac{\sqrt{169}}{\sqrt{9}}=\frac{13}{3}=4\frac{1}{3}$  

---

$\text{h)}\sqrt{7\frac{9}{16}}=\sqrt{\frac{121}{16}}=\frac{\sqrt{121}}{\sqrt{16}}=\frac{11}{4}=2\frac{3}{4}$