Finding Consecutive Integers for Square Root of 130

The problem asks us to find two consecutive integers between which the value of lies.
To do this, we need to find the perfect squares that are closest to 130.

Let’s list some perfect squares:

We can see that 130 is between 121 and 144.
So, .

Taking the square root of all parts of the inequality, we get:

We know that and .
Therefore, .

This means that the value of lies between the two consecutive integers 11 and 12.

We are asked to plot two points that represent these consecutive integers on the number line. The number line provided shows integers from 0 to 20. We need to locate the points corresponding to 11 and 12 on this number line.

The final answer is .