There are many ways to do it. Have a look at the Wikipedia article (check the link).
See the related link for a detailed description of a manual method for calculating square roots.
No.
Because many square roots are irrational numbers that can not be computed to an exact value for lack of space to continue an infinite string of digits after the decimal point.
Well, it's both: you're using a machine to compute an approximation. Why isn't it exact? Most square roots (such as the square root of two) are irrational numbers, so their decimal representation requires an infinite number of digits. We humans have to have finite answers, hence we round off.
Your brain, of course.
Usually with great difficulty. The answer also depends on the nature of the irrational number - whether it is simply a square root or if it is a combination of roots of different orders.
See the related link for a detailed description of a manual method for calculating square roots.
No.
Because many square roots are irrational numbers that can not be computed to an exact value for lack of space to continue an infinite string of digits after the decimal point.
Square roots are computed using the Babylonian method, calculators, Newton's method, or the Rough estimation method. * * * * * Or the Newton-Raphson method.
Numbers like 10, 25, 50, and 100 are easy to compute mentally because they have simple multiples or divisions that are easy to work with. For example, doubling 25 is 50, or dividing 100 by 10 gives you 10. These numbers are often used as benchmarks in mental math calculations.
Well, it's both: you're using a machine to compute an approximation. Why isn't it exact? Most square roots (such as the square root of two) are irrational numbers, so their decimal representation requires an infinite number of digits. We humans have to have finite answers, hence we round off.
benchmark numbers
It depends on your computational skills.
Your brain, of course.
compatible numbers
if you mean multiplication then 4x25=100 x 27 = 270