14. Sketch and label a figure to demonstrate that \( \sqrt{45} \) is equivalent to \( 3 \sqrt{5} \). (Use square dot paper or graph paper.)

To visualize that \( \sqrt{45} \) is equivalent to \( 3 \sqrt{5} \), imagine a square with an area of 45 square units. The side length of this square will be \( \sqrt{45} \). Now, we can also express \( \sqrt{45} \) as \( \sqrt{9 \times 5} \), which simplifies to \( \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \). Draw a square with \( 45 \) units area and divide it into smaller squares (9 of side 1 unit each) and rectangles (to depict \( \sqrt{5} \)). Label the side lengths to show how they correspond to both representations. To further understand the equivalence, use graph paper to draw a large square (side length \( \sqrt{45} \)) and inside it, create three smaller square sections, each with area \( 5 \) (side length \( \sqrt{5} \)). This not only illustrates the relationship between the numbers visually but also solidifies the concept that both expressions represent the same geometric dimension!