$\text{a)}$

$\sqrt{8\cdot {10}^5\cdot 1,8\cdot {10}^8}$ $=\sqrt{14,4\cdot {10}^{13}}=$

$=\sqrt{144\cdot {10}^{12}}=\sqrt{144}\cdot \sqrt{\left({10}^{12}\right)}=12\cdot {10}^6$   

 

$\text{b)}$

$\sqrt{8\cdot {10}^8\cdot 5\cdot {10}^{13}}=\sqrt{40\cdot {10}^{21}}=\sqrt{4\cdot 10\cdot {10}^{21}}=$

$=\sqrt{4\cdot {10}^{22}}=\sqrt{4}\cdot \sqrt{{10}^{22}}=2\cdot {10}^{11}$