1. The problem is to evaluate the expression $0.9 \sqrt{0.51}$. 2. Recall that the square root function $\sqrt{x}$ gives the positive number which, when squared, equals $x$. 3. First, calculate $\sqrt{0.51}$. 4. Using a calculator or approximation, $\sqrt{0.51} \approx 0.714$. 5. Now multiply $0.9$ by $0.714$: $$0.9 \times 0.714 = 0.6426$$ 6. Therefore, the value of $0.9 \sqrt{0.51}$ is approximately $0.6426$. 7. This means the expression evaluates to about $0.6426$ when rounded to four decimal places.