(2)^(1/2) = 1.414

Representing 1.5 and 2√2 on the same number line helps us understand their relative positions and compare their magnitudes. Let's break down the process step by step:

- First, we need to understand the concept of a number line. A number line is a straight line on which numbers can be placed to represent their magnitude and relative positions. It extends infinitely in both directions, with zero in the middle.

- To represent 1.5 on the number line, we start at zero and move towards the positive side. Since 1.5 is a positive number, we move to the right. We can divide the space between zero and 1 into equal parts, and since 1.5 is halfway between 1 and 2, we place it exactly in the middle of this space. So, we locate 1.5 on the number line.

- Next, let's represent 2√2 on the number line. Here, we have a square root (√) and a coefficient of 2. To simplify this, we need to calculate the value of √2. The square root of 2 is approximately 1.41. Multiplying this by 2 gives us 2.82. So, 2√2 is approximately 2.82.

- Now, we can place 2√2 on the number line. Since it is a positive number, we move to the right from zero. Using the same method as before, we divide the space between 2 and 3 into equal parts, and since 2√2 is closer to 3, we place it slightly to the left of the midpoint. So, we locate 2√2 on the number line.

- Finally, we can compare the positions of 1.5 and 2√2 on the number line. By visually inspecting the number line, we can see that 2√2 is larger than 1.5. The distance between 2√2 and 3 is smaller than the distance between 1.5 and 2. This indicates that 2√2 is closer to 2 than 1.5 is to 2.

In conclusion, representing 1.5 and 2√2 on the same number line allows us to compare their magnitudes and understand their relative positions. It helps visualize their distances from specific points, such as zero or other reference numbers, aiding in numerical comparisons and calculations.

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