Question

Using a number line, what is the approximate value of 19−−√ ?(1 point) Responses 4.38 4.38 4.25 4.25 4.13 4.13 4.5

Answer 1

To find the approximate value of \(\sqrt{19}\) using a number line, we can look for square numbers close to 19.

We know:
- \(4^2 = 16\)
- \(5^2 = 25\)

This means:
- \(\sqrt{16} = 4\)
- \(\sqrt{25} = 5\)

Since \(19\) is between \(16\) and \(25\), it follows that \(\sqrt{19}\) is between \(4\) and \(5\).

To narrow it down further:
- The square of \(4.4\) is \(4.4^2 = 19.36\) (which is greater than 19),
- The square of \(4.3\) is \(4.3^2 = 18.49\) (which is less than 19).

This means that \(\sqrt{19}\) is between \(4.3\) and \(4.4\). A good estimate for \(\sqrt{19}\) would then be close to \(4.35\).

Among the options given:
- 4.38
- 4.25
- 4.13
- 4.5

The value \(4.38\) is the closest approximation to \(\sqrt{19}\). Therefore, the best response is:

**4.38**