To represent √2 on a number line, we need to understand what √2 represents and then locate it accurately. Let's break down the process into several steps.

Understanding √2:
- The symbol √ is called the square root symbol, and it denotes the principal square root of a number.
- The number 2 inside the square root symbol (√2) represents the radicand, which is the number we are finding the square root of.
- The square root (√) of a number is the value that, when multiplied by itself, gives the radicand. In this case, we are finding the value that, when multiplied by itself, gives 2.

Steps to represent √2 on a number line:

1. Draw the number line:
- Start by drawing a straight line horizontally.
- Label the line with numbers, ensuring that the line extends far enough in both directions to accommodate the range needed to represent √2.

2. Locate the number 1:
- Mark a point labeled "1" on the number line. This is our starting point.

3. Determine an approximate location for √2:
- Since √2 is an irrational number, its decimal representation goes on indefinitely without repeating. However, we can approximate its value.
- √2 is between 1 and 2, so we need to find a value between these two numbers.
- We can estimate that √2 is approximately 1.4.

4. Locate the approximate point:
- Measure a distance of 1.4 units to the right of the point labeled "1" on the number line.
- Mark a point at this location and label it "√2" or "1.4."

5. Verify the accuracy:
- To confirm the accuracy of the representation, we can calculate the square of the approximate point.
- Multiply 1.4 by itself and verify that it equals 2 (1.4 * 1.4 = 1.96, which is close to 2).

By following these steps, we can represent √2 on a number line. It's important to note that while the representation is an approximation, it allows us to visualize the location of √2 relative to other numbers on the number line.