how do I estimate the value of a square root to one decimal place without a calculator

Question

 I need to estimate the value of a square root to one decimal place without a calculator

Answer 1

By a series of guess-and-check operations.

 

What square root of 19?

First guess 5; 5 squared is 25--too high so let's try 4.5 (since 4 squared is only 16).

4.5 squared is 20.25... much better, but too high.

Next guess: 4.4; 4.4 squared is 19.36

 

What do you think the next guess ought to be?

 

Et cetera, etc.