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
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