using a number line, what is the approximate value of 39−−√ ?(1 point)

Answer 1

To find the approximate value of $\sqrt{39}$ using a number line, we can identify two perfect squares between which 39 falls.

The perfect squares are:

• $6^2=36$
• $7^2=49$

This means that $\sqrt{39}$ will be between 6 and 7. To get a more precise approximation, we can compare it to numbers like 6.1 and 6.2.

Calculating these:

• ${6.1}^2=37.21$
• ${6.2}^2=38.44$
• ${6.3}^2=39.69$

Thus, $\sqrt{39}$ is between $6.2$ and $6.3$. Since $39$ is closer to $36$ than to $49$, we can refine it further and estimate $\sqrt{39}\approx 6.24$.

On a number line, you would place $\sqrt{39}$ a little to the right of 6.2 and a little to the left of 6.3, approximately around 6.24.