1. **State the problem:** Evaluate $$\sqrt{\frac{1}{24.56} + 4.346^2}$$ correct to 4 significant figures. 2. **Recall formulas and rules:** - Reciprocal: $$\frac{1}{x}$$ means dividing 1 by the number $$x$$. - Square: $$a^2 = a \times a$$. - Square root: $$\sqrt{x}$$ is the number which when squared gives $$x$$. 3. **Calculate the reciprocal:** $$\frac{1}{24.56} \approx 0.04072$$ (4 significant figures). 4. **Calculate the square:** $$4.346^2 = 4.346 \times 4.346 = 18.889$$ (4 significant figures). 5. **Add the two results:** $$0.04072 + 18.889 = 18.9297$$. 6. **Calculate the square root:** $$\sqrt{18.9297} \approx 4.350$$ (4 significant figures). **Final answer:** $$4.350$$