Identify whether the number is a perfect square
If it is a perfect square, take the square root directly
If it is not a perfect square, use one of these methods:
Prime factorization method
Factor the number into primes
Pair identical prime factors
Multiply one factor from each pair
Estimation method
Find the nearest perfect squares on either side
Narrow the interval and refine until the desired accuracy is reached
Long division (digit-by-digit) method
Group digits in pairs from the decimal point outward
Find the next digit of the root by trial and subtraction
Continue until the required decimal places are obtained
Using a calculator
Use the square root function (√) or exponent 0.5
For negative numbers
No real square root exists
Use complex form: √(-a) = i√a