Step 1: Convert the mixed number to an improper fraction. $$1\frac{1}{16} = \frac{1 \times 16 + 1}{16} = \frac{17}{16}$$ Step 2: Find the square root of the improper fraction. $$\sqrt{\frac{17}{16}} = \frac{\sqrt{17}}{\sqrt{16}}$$ $$\frac{\sqrt{17}}{4}$$ The value is $\boxed{\frac{\sqrt{17}}{4}}$. Step 1: Perform the division. When a number is divided by itself, the result is 1, provided the number is not zero. $$\frac{3}{729} \div \frac{3}{729} = 1$$ Alternatively, invert the second fraction and multiply: $$\frac{3}{729} \times \frac{729}{3} = \frac{3 \times 729}{729 \times 3} = 1$$ The simplified expression is $\boxed{1}$. Step 1: Recall the properties of a kite. A kite is a quadrilateral with two distinct pairs of equal-length adjacent sides. This means that if the sides are 7 cm and 9 cm, there are two sides of length 7 cm and two sides of length 9 cm. Step 2: Calculate the perimeter. The perimeter is the sum of the lengths of all sides. $$\text{Perimeter} = 7 \text{ cm} + 7 \text{ cm} + 9 \text{ cm} + 9 \text{ cm}$$ $$\text{Perimeter} = 2(7 \text{ cm}) + 2(9 \text{ cm})$$ $$\text{Perimeter} = 14 \text{ cm} + 18 \text{ cm}$$ $$\text{Perimeter} = 32 \text{ cm}$$ The perimeter of the kite is $\boxed{32 \text{ cm}}$.