1. **State the problem:** We need to find the difference in lengths between two beams, one of length $\sqrt{72}$ meters and the other $\sqrt{18}$ meters. 2. **Recall the formula:** The difference in lengths is given by $$\text{Difference} = \sqrt{72} - \sqrt{18}$$ 3. **Simplify each square root:** - $\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$ - $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$ 4. **Calculate the difference:** $$6\sqrt{2} - 3\sqrt{2} = (6 - 3)\sqrt{2} = 3\sqrt{2}$$ 5. **Interpretation:** The difference in lengths is $3\sqrt{2}$ meters. **Final answer:** $3\sqrt{2}$ meters.