Using a number line, what is the approximate value of 19−−√

Question

?(1 point)
Responses

4.5
4.5

4.25
4.25

4.13
4.13

4.38

Answer 1

To determine the approximate value of \(\sqrt{19}\) using a number line, we need to identify the perfect squares around 19.

• The square of 4 is \(4^2 = 16\).
• The square of 5 is \(5^2 = 25\).

Since \(16 < 19 < 25\), we know that \(4 < \sqrt{19} < 5\).

Next, let's further inspect to find a value between 4 and 5:

• The square of 4.5 is \(4.5^2 = 20.25\), which is greater than 19.
• The square of 4.4 is \(4.4^2 = 19.36\), which is also greater than 19.
• The square of 4.3 is \(4.3^2 = 18.49\), which is less than 19.

This shows that \(\sqrt{19}\) is between 4.3 and 4.4.

Since you're looking at specific options to choose from, the value closest to our findings for \(\sqrt{19}\) is approximately 4.38.

Therefore, the best response from the options provided is 4.38.