on a number line:
To approximate a square root we need to find two perfect squares: one bigger and one smaller than our radicand. Then the approximation of the square root is going to be between the two numbers.
Example 1) Plot on a number line:
We have to find the two closest numbers to 22 that are perfect squares. The closest number smaller than 22 that has an integer square root is 16 and the closest number greater than 22 that has an integer square root is 25.
16 < 22 < 25
4 < 
< 5
So 
is somewhere between 4 and 5. Since 22 is closer to 25 than 16, the point should be plotted closer to 5.
Example 2) Plot 
on a number line.
We start by finding perfect squares close to 13. The closest perfect squares to 13 are 9 and 16.
Now we have:
9 < 13 < 16
We just have to perform all operations done in the original square root expression to all three sides of this inequality:
