If x is a number, the square root of a number is derived from
1) Without using the calculator, it's not difficult to find the square root if you memorize the perfect square. This is possible with practice.
Example: 4 (2×2), 9 (3×3) , 16 (4×4), 25 (5×5), 36 (6×6), 49 (7×7)
2) If the the radicand is not a perfect square, try breaking it down to its factors, where one of the factors is a perfect square.
48 is not a perfect square
The factors of 48 are:
12 and 4
16 and 3
8 and 6
Among the set of factors, 16 and 3 are factors where a factor is a perfect square which is 16.
3) If the radicand is a prime number, then the radical is in simplified form, unless you are instructed to get the square root using calculator.
4) If the radicand can not be factored in such a way that none of its factors is a perfect square, then the radical number is in simplified form, unless you are instructed to get the square root using the calculator.
5). If the radicand is a negative number, follow item number 2 above, but the factor that is not a perfect square is the negative factor; it is written as imaginary number "i".