Using a number line, what is the approximate value of 19−−√ ?(1 point)

Question

Responses

4.25
4.25

4.5
4.5

4.13
4.13

4.38

Answer 1

To find the approximate value of \(\sqrt{19}\), let's analyze the values of perfect squares around 19:

• \(4^2 = 16\)
• \(5^2 = 25\)

This means \(\sqrt{19}\) is between 4 and 5.

Next, to narrow it down further:

• \(4.3^2 = 18.49\)
• \(4.4^2 = 19.36\)

Thus, \(\sqrt{19}\) is between 4.3 and 4.4.

Now, checking a value in the middle:

• \(4.35^2 = 18.9225\) (is less than 19)
• \(4.36^2 = 19.0496\) (is greater than 19)

Hence, \(\sqrt{19}\) is approximately 4.36.

Among the options given, 4.38 is the closest approximation.

The answer is 4.38.