Understanding Square Root of 5 on a Number Line
To find the square root of 5 on a number line, follow these detailed steps:
Step 1: Identify Key Points
- Locate the integers 2 and 3 on the number line.
- Since 2² = 4 and 3² = 9, it follows that √5 lies between 2 and 3.
Step 2: Create a Scale
- Divide the section between 2 and 3 into ten equal parts.
- Each part represents 0.1, allowing for precise placement.
Step 3: Estimate the Value
- Start by estimating where √5 might be.
- Since √5 is closer to 2 than to 3, begin your estimation near 2.
Step 4: Refine Your Estimate
- Test the value of 2.2:
- 2.2² = 4.84 (too low)
- Next, test 2.3:
- 2.3² = 5.29 (too high)
- Since √5 is between 2.2 and 2.3, continue refining.
Step 5: Pinpoint the Value
- Try 2.24:
- 2.24² = 5.0176 (too high)
- Then try 2.23:
- 2.23² = 4.9729 (too low)
- Thus, √5 is approximately 2.23, which you can place on the number line.
Conclusion
- Mark the point corresponding to 2.23 on the number line.
- This method allows for a visual and intuitive understanding of √5 and its placement between 2 and 3.