Question

Using a number line, what is the approximate value of sqrt 19? A. 4.13 B. 4.25 C. 4.5 D. 4.38

Answer 1

To estimate \( \sqrt{19} \) using a number line, we need to find two perfect squares that \( 19 \) lies between.

The perfect squares closest to \( 19 \) are:
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)

This means:
\[
4 < \sqrt{19} < 5
\]

Now we can narrow it down further. Let's check the squares of numbers between \( 4 \) and \( 5 \):

- \( 4.1^2 = 16.81 \) (too low)
- \( 4.2^2 = 17.64 \) (too low)
- \( 4.3^2 = 18.49 \) (too low)
- \( 4.4^2 = 19.36 \) (too high)

From this, we see that \( \sqrt{19} \) is between \( 4.3 \) and \( 4.4 \).

Now let's consider the options given:

A. 4.13
B. 4.25
C. 4.5
D. 4.38

Since \( \sqrt{19} \) is approximately between \( 4.3 \) and \( 4.4 \), the closest option is:

**D. 4.38**

This is the best approximation of \( \sqrt{19} \) from the options provided.