Dividing Radicals

  1. $\dfrac{\sqrt{10}}{\sqrt{5}}\times \dfrac{\sqrt{5}}{\sqrt{5}}=\dfrac{5\sqrt{2}}{5}=\sqrt{2}$
  2. $\dfrac{\sqrt{8}}{\sqrt{32}}=\dfrac{2\sqrt{2}}{4\sqrt{2}}=\dfrac{2}{4}=\dfrac{1}{2}$
  3. $\dfrac{\sqrt{3}}{\sqrt{20}}=\dfrac{\sqrt{3}}{2\sqrt{5}}\times \dfrac{\sqrt{5}}{\sqrt{5}}=\dfrac{\sqrt{15}}{10}$
  4. $\dfrac{\sqrt{28}}{\sqrt{6}}=\dfrac{2\sqrt{7}}{\sqrt{6}} \times \dfrac{\sqrt{6}}{\sqrt{6}}=\dfrac{2\sqrt{42}}{6}=\dfrac{\sqrt{42}}{3}$
  5. $\dfrac{\sqrt{15}}{\sqrt{45}}=\dfrac{\sqrt{3}\sqrt{5}}{3\sqrt{5}}=\dfrac{\sqrt{3}}{3}$
  6. $\dfrac{\sqrt{96}}{\sqrt{18}}=\dfrac{4\sqrt{2}\sqrt{3}}{3\sqrt{2}}=\dfrac{4\sqrt{3}}{3}$
  7. $\dfrac{\sqrt{40}}{\sqrt{5}}=\dfrac{2\sqrt{2}\sqrt{5}}{\sqrt{5}}=2\sqrt{2}$
  8. $\dfrac{\sqrt{21}}{\sqrt{7}}=\dfrac{\sqrt{3}\sqrt{7}}{\sqrt{7}}=\sqrt{3}$
  9. $\dfrac{\sqrt{5}}{\sqrt{30}}=\dfrac{\sqrt{5}}{\sqrt{5}\sqrt{6}}=\dfrac{1}{\sqrt{6}} \times \dfrac{\sqrt{6}}{\sqrt{6}} = \dfrac{\sqrt{6}}{6}$
  10. $\dfrac{\sqrt{11}}{\sqrt{88}}=\dfrac{\sqrt{11}}{2\sqrt{2}\sqrt{11}}=\dfrac{1}{2\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{2}}{4}$
  11. $\dfrac{\sqrt{54}}{\sqrt{6}}=\dfrac{3\sqrt{6}}{\sqrt{6}}=3$
  12. $\dfrac{\sqrt{2}}{\sqrt{15}} \times \dfrac{\sqrt{15}}{\sqrt{15}}=\dfrac{\sqrt{30}}{15}$
  13. $\dfrac{\sqrt{24}}{\sqrt{2}} =\dfrac{2\sqrt{6}}{\sqrt{2}}=\dfrac{2\sqrt{2}\sqrt{3}}{\sqrt{2}}=2\sqrt{3}$
  14. $\dfrac{\sqrt{3}}{\sqrt{27}}=\dfrac{\sqrt{3}}{3\sqrt{3}}=\dfrac{1}{3}$
  15. $\dfrac{\sqrt{5}}{\sqrt{35}}=\dfrac{\sqrt{5}}{\sqrt{5}\sqrt{7}}=\dfrac{1}{\sqrt{7}}\times \dfrac{\sqrt{7}}{\sqrt{7}}=\dfrac{\sqrt{7}}{7}$
  16. $\dfrac{\sqrt{42}}{\sqrt{3}}=\dfrac{\sqrt{3}\sqrt{14}}{\sqrt{3}}=\sqrt{14}$
  17. $\dfrac{\sqrt{72}}{\sqrt{12}}=\dfrac{6\sqrt{2}}{2\sqrt{3}}=\dfrac{3\sqrt{2}}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{3\sqrt{6}}{3}=\sqrt{6}$
  18. $\dfrac{\sqrt{14}}{\sqrt{7}}=\dfrac{\sqrt{2}\sqrt{7}}{\sqrt{7}}=\sqrt{2}$
  19. $\dfrac{\sqrt{13}}{\sqrt{26}}=\dfrac{\sqrt{13}}{\sqrt{2}\sqrt{13}}=\dfrac{1}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}$
  20. $\dfrac{\sqrt{56}}{\sqrt{6}}= \dfrac{2\sqrt{2}\sqrt{7}}{\sqrt{2}\sqrt{3}}=\dfrac{2\sqrt{7}}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{2\sqrt{21}}{3}$