Using a number line,what is the approximate value of square root 19?

Question

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

Answer 1

To approximate the value of $\sqrt{19}$ using a number line, we can first identify the squares of whole numbers around 19.

• $4^2=16$
• $5^2=25$

Since $19$ is between $16$ and $25$, we know that:

$$4<\sqrt{19}<5$$

Next, we can check some decimal values between $4$ and $5$:

• ${4.25}^2=18.0625$
• ${4.5}^2=20.25$
• ${4.4}^2=19.36$
• ${4.38}^2\approx 19.0244$
• ${4.3}^2=18.49$

From these calculations, we can see that:

• ${4.38}^2$ is a close approximation, being just above $19$.
• ${4.4}^2$ is above $19$, while ${4.3}^2$ is below $19$.

Given these estimates, the best choice among the options provided is $C.4.38$, as it gives a value very close to $\sqrt{19}$.

Thus, the approximate value of $\sqrt{19}$ is:

C. 4.38