Question

\sqrt(39) locate on number line

Answer 1

To locate \(\sqrt{39}\) on a number line, we can start by estimating its value.

1. **Find perfect squares around 39**:
- \(6^2 = 36\)
- \(7^2 = 49\)

This tells us that \(\sqrt{39}\) is between 6 and 7, since \(6^2 < 39 < 7^2\).

2. **Narrow down the estimate**:
- We can check the midpoints to get a more precise value.
- \(6.2^2 = 38.44\) (less than 39)
- \(6.3^2 = 39.69\) (greater than 39)

So, \(\sqrt{39}\) is between 6.2 and 6.3.

3. **Further refinement**:
- Check \(6.24^2 = 38.4976\) (less than 39)
- Check \(6.25^2 = 39.0625\) (greater than 39)

This indicates that \(\sqrt{39}\) is between 6.24 and 6.25.

4. **Calculate approximately**:
Using a calculator, we find that \(\sqrt{39} \approx 6.244\).

5. **Marking on the number line**:
On a number line, you would:
- Locate the points for 6, 6.2, 6.3, and mark your approximate position for \(\sqrt{39}\) just slightly to the right of 6.24.

By following the steps above, you can accurately place \(\sqrt{39}\) on the number line!