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.
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
Your brain, of course.
It depends on your computational skills.
if you mean multiplication then 4x25=100 x 27 = 270
compatible numbers
The patterns and properties to compute mentally 120 times 30 is the numbers 12 and 3 plus the two 0. Multiply 12 by 3 (36) and add the two 0 (3600).