When can you use the square roots of perfect squares to determine the perfect roots of decimals ?

If you want to find the decimal value of a square root, you can use the 2 closest perfect squares to them.

Example

Approximate the value of sqrt20

Pick the 2 closest perfect squares, one before and one after 20:

16 and 25.

So, the square root of 20 has to be between 4 and 5.

Since 20 is closer to 16 than it is to 25,

We can estimate the decimal value of sqrt20 to be around 4.4

Distance=slopeslope is -2/4which equals-1/2the distance between these two points is -1/2