#18) (√2)/(2y)
#19) 7x/5
#20) (2√5)/5
#21) (3√5)/5
#22) √5/b
#23) (2√(2n))/n
#24) (2√15)/15m
For #18:
[tex]\sqrt{\frac{18y}{36y^3}}=\sqrt{\frac{1}{2y^2}}=\frac{1}{y\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2y}[/tex]
#19:
[tex]\sqrt{\frac{49x^5}{25x^3}}=\sqrt{\frac{49x^2}{25}}=\frac{7x}{5}[/tex]
#20:
[tex]\frac{\sqrt{12}}{\sqrt{15}}=\frac{2\sqrt{3}}{\sqrt{15}}\times \frac{\sqrt{15}}{\sqrt{15}}=\frac{2\sqrt{45}}{15}=\frac{6\sqrt{5}}{15}=\frac{2\sqrt{5}}{5}[/tex]
#21:
[tex]\frac{\sqrt{72}}{\sqrt{40}}=\frac{6\sqrt{2}}{2\sqrt{10}}=\frac{3\sqrt{2}}{\sqrt{10}}\times \frac{\sqrt{10}}{\sqrt{10}}=\frac{3\sqrt{20}}{10}=\frac{6\sqrt{5}}{10}=\frac{3\sqrt{5}}{5}[/tex]
#22:
[tex]\sqrt{\frac{25b}{5b^3}}=\sqrt{\frac{5}{b^2}}=\frac{\sqrt{5}}{b}[/tex]
#23:
[tex]\sqrt{\frac{24}{3n}}=\sqrt{\frac{8}{n}}=\frac{2\sqrt{2}}{\sqrt{n}}\times \frac{\sqrt{n}}{\sqrt{n}}=\frac{2\sqrt{2n}}{n}[/tex]
#24:
[tex]\sqrt{\frac{8}{30m^2}}=\sqrt{\frac{4}{15m^2}}=\frac{2}{m\sqrt{15}}\times \frac{\sqrt{15}}{\sqrt{15}}=\frac{2\sqrt{15}}{15m}[/tex]
