Question: how do you work out the square root without a calculator?
Answer: Examples.
Finding square roots of of numbers that aren't perfect squares without a calculator.
Example: Calculate the square root of 10 ( ) to 2 decimal places.
Find the two perfect square numbers it lies between.
Divide 10 by 3. ... 
Average 3.33 and 3. ( ... 
Repeat step 2: 10/3.1667 = 3.1579.