To find the square root of a very large number you would do prime factorization, or a factor tree.
For example: find the square root of 1800
1800/2 = 900
900 /2 = 450
450 / 2 = 225
225/ 5 = 45
45/5 = 9
9/3 = 3
2 * 2 * 2 * 5 * 5 * 3 * 3
Now match pairs of two.
2 * 5 * 3 sqrt(2)
30sqrt(2)