There are several methods to calculate a root square.

— By hand framing: the classic method is to estimate the value by calculating which integers squared would give a minimum interval.

Example: Enclosing $ \sqrt{8} $: $ 2^2 = 4 < 8 < 9 = 3^3 $ so $ 2 < \sqrt{8} < 3 $, it is then possible to enclose the first digit after the comma: $ 2.8^2 < 8 < 2.9^2 $ etc.

— By extraction of squares: if the number under the root is factorized with squares, then it is possible to extract them from the root.

Example: Factorization of $ \sqrt{8} = \sqrt{ 4 \times 2 } = \sqrt{ 2^2 \times 2 } = 2 \sqrt{2} $. Since $ \sqrt{2} \approx 1.414 $, then $ \sqrt{8} \approx 2.828 $

— With a square root calculator like this one from dCode:

Enter a positive or negative number (in this case, it will have complex roots).

Choose the format of the result, either an exact value (if it is an integer or variables) or approximate (decimal number with adjustable precision by defining a minimum number of significant digits)

Example: $ \sqrt{12} = 2 \sqrt{3} \approx 3.464 $

Example: $ \sqrt{-1} = i $ (complex root)