Step 1: Convert the decimal under the square root to a fraction. $$ 0.00000225 = \frac{225}{100,000,000} $$ Step 2: Calculate the square root of the numerator and the denominator separately. $$ \sqrt{225} = 15 $$ $$ \sqrt{100,000,000} = \sqrt{10^8} = 10^{\frac{8}{2}} = 10^4 = 10,000 $$ Step 3: Substitute these values back into the square root expression. $$ \sqrt{0.00000225} = \sqrt{\frac{225}{100,000,000}} = \frac{\sqrt{225}}{\sqrt{100,000,000}} = \frac{15}{10,000} $$ Step 4: Substitute this result back into the original problem. $$ \frac{\frac{15}{10,000}}{15} $$ Step 5: Simplify the complex fraction. $$ \frac{15}{10,000} \times \frac{1}{15} = \frac{1}{10,000} $$ Step 6: Convert the fraction to a decimal. $$ \frac{1}{10,000} = 0.0001 $$ The answer is $\boxed{0.0001}$.