**Locating √3 on a Number Line**

To locate the square root of 3 (√3) on a number line, we can follow a step-by-step process. Here's how:

**Step 1: Understand the Basics**
Before we start, let's quickly revise some basic concepts related to number lines and square roots:

- A number line is a straight line that represents numbers in order, with equal intervals between them.
- The square root (√) of a number is a value that, when multiplied by itself, gives the original number.

**Step 2: Set Up the Number Line**
To begin, draw a horizontal line that represents the number line. Ensure you have enough space to accommodate the range of numbers you'll be working with.

**Step 3: Determine the Interval**
Next, determine the interval or scale for the number line. This is the distance between each unit on the line. For simplicity, let's assume the interval is 1 unit.

**Step 4: Locate Whole Numbers**
Mark the whole numbers on the number line by labeling each interval with the corresponding whole numbers (e.g., 0, 1, 2, 3, etc.). Ensure that the intervals are evenly spaced.

**Step 5: Locate Perfect Squares**
Identify the perfect squares (numbers that have whole number square roots) that are closest to 3. In this case, the perfect squares closest to 3 are 1 and 4.

**Step 6: Locate √3**
To locate √3 on the number line, we need to estimate its position between the perfect squares 1 and 4:

- Since 3 is greater than 1 and less than 4, we know that √3 will lie between the square roots of these numbers (√1 and √4).
- The square root of 1 (√1) is 1, and the square root of 4 (√4) is 2.
- Therefore, √3 would be positioned between 1 and 2 on the number line.

**Step 7: Estimate the Position**
To make a more accurate estimation, divide the interval between 1 and 2 into smaller intervals. If we divide it into 10 equal parts, each part would represent 0.1 units.

**Step 8: Locate √3 Precisely**
Since √3 lies between 1 and 2, it will be closer to 2. By estimation, √3 is approximately 1.7. To locate it more precisely, we can divide the interval between 1 and 2 into smaller intervals:

- Mark the point 1.7 units from 1, which represents √3 on the number line.
- Label this point as √3.

**Conclusion**
By following these steps, we can locate √3 on a number line with reasonable accuracy. Remember that the square root of 3 is an irrational number, so it cannot be expressed as a simple fraction or decimal. However, by estimating its position between perfect squares and using intervals on the number line, we can determine its approximate location.

Draw a line 1 cm oa and cut an arc ab is 1 cm join ob and b is a point draw an right angle and cut an arc bc is 1 cm join co . open the compass o to c and cut an arc on number line. this point is root 3 on a number line this method name is spiral sqare root.