1. **Problem statement:** Find the value of $n$ given the expression $n = \sqrt{v} \times 7 \times 4$ and the value of $v = 9 \times 7 \times 8 - \sqrt{18}$. 2. **Calculate $v$ first:** Calculate the product $9 \times 7 \times 8$: $$9 \times 7 = 63$$ $$63 \times 8 = 504$$ Calculate $\sqrt{18}$: $$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \approx 4.2426$$ So, $$v = 504 - 3\sqrt{2} \approx 504 - 4.2426 = 499.7574$$ 3. **Calculate $\sqrt{v}$:** $$\sqrt{499.7574} \approx 22.355$$ 4. **Calculate $n$ using the formula:** $$n = \sqrt{v} \times 7 \times 4 = 22.355 \times 7 \times 4$$ Multiply stepwise: $$22.355 \times 7 = 156.485$$ $$156.485 \times 4 = 625.94$$ 5. **Final answer:** $$\boxed{n \approx 625.94}$$ This means the value of $n$ is approximately 625.94 based on the given expressions.