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To find an approximate value for the square root of a number N, you can find the closest square number smaller than N and the closest square number larger than N. The square roots of the square numbers will be easy to calculate and should be 1 apart. The square root of N will be some number between the square roots of each square. To find N by trial and error you could then just try different numbers from this range and check if it’s square is close to N. For example, the square root of 10 lies between 3 (because 3^2=9) and 4 (because 4^2=16). So we can try squaring numbers between 3 and 4 to find a value close to 10, and this will approximately be the square root of 10. As it has already been said, it is not necessary to do this all the time. However, it’s a good thought experiment to choose a number and try to approximate the square root of that number, to test your understanding of squares and square roots.
The square root by hand is not a very difficult process however it is a skill no longer required or taught in general education. The best way now is by use of calculator
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