Ta có :

a.  $\frac{\sqrt{2}}{\sqrt{18}}=\sqrt{\frac{2}{18}}=\sqrt{\frac{1}{9}}=\frac{1}{3}$

Vậy $\frac{\sqrt{2}}{\sqrt{18}}=\frac{1}{3}$

b.  $\frac{\sqrt{15}}{\sqrt{735}}=\sqrt{\frac{15}{735}}=\sqrt{\frac{1}{49}}=\frac{1}{7}$

Vậy $\frac{\sqrt{15}}{\sqrt{735}}=\frac{1}{7}$

c.  $\frac{\sqrt{12500}}{\sqrt{500}}=\sqrt{\frac{12500}{500}}=\sqrt{25}=5$

Vậy $\frac{\sqrt{12500}}{\sqrt{500}}=5$

d.  $\frac{\sqrt{65}}{\sqrt{2^{3}.3^{5}}}=\sqrt{\frac{65}{2^{3}.3^{5}}}$

<=> $\sqrt{\frac{2^{5}.3^{5}}{2^{3}.3^{5}}}=\sqrt{\frac{2^{5}}{2^{3}}}=\sqrt{2^{2}}=2$

Vậy $\frac{\sqrt{65}}{\sqrt{2^{3}.3^{5}}}=2$