Question

Using A Number Line, What Is The Approximate Value Of Square Root Of √19 ? a. 4.13 b. 4.38 c. 4.5 d. 4.25

Answer 1

To find the approximate value of the square root of 19 (√19) using a number line, we can start by identifying the perfect squares around 19.

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

This means that \(4 < \sqrt{19} < 5\).

Next, we can calculate the squares of decimal numbers between 4 and 5 to narrow it down further:

- \(4.4^2 = 19.36\) (too high)
- \(4.3^2 = 18.49\) (too low)
- \(4.35^2 ≈ 18.9225\) (too low)
- \(4.38^2 ≈ 19.1844\) (too high)

From this, we determine that \(\sqrt{19}\) is between 4.3 and 4.4. Looking at your options:
a. 4.13
b. 4.38
c. 4.5
d. 4.25

Since we've established that \(\sqrt{19}\) is greater than 4.3 and less than 4.4, the best approximation from the choices provided is **b. 4.38**.