1. **State the problem:** Simplify the expression $$\sqrt{\frac{35}{20}}$$. 2. **Recall the property of square roots:** $$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$$ for positive numbers $a$ and $b$. 3. **Apply the property:** $$\sqrt{\frac{35}{20}} = \frac{\sqrt{35}}{\sqrt{20}}$$ 4. **Simplify the square roots by factoring:** - $35 = 7 \times 5$ - $20 = 4 \times 5$ 5. **Rewrite the expression:** $$\frac{\sqrt{7 \times 5}}{\sqrt{4 \times 5}} = \frac{\sqrt{7} \times \sqrt{5}}{\sqrt{4} \times \sqrt{5}}$$ 6. **Cancel common factors:** $$\frac{\sqrt{7} \times \cancel{\sqrt{5}}}{2 \times \cancel{\sqrt{5}}} = \frac{\sqrt{7}}{2}$$ 7. **Final simplified form:** $$\sqrt{\frac{35}{20}} = \frac{\sqrt{7}}{2}$$ This means the square root of the fraction simplifies to half the square root of 7.