How do you find square root of a no?

Answer 1

1) The best method is usually to use a calculator that has the square root function (i.e., just about any calculator), since the other methods are quite cumbersome.

2) You can try squaring different numbers. If you want the square root of 2, 1.4 squared is 1.96, while 1.5 squared is 2.25, so the actual square root must be somewhere between 1.4 and 1.5. Continue experimenting with 1.45, 1.42, etc.

3) If you have an approximation to a square root, you can get a better approximation as follows. As an example, let's say that your approximation for the square root of 2 is 1.4. Now, divide 2 / 1.4. The answer is approximately 1.428. Since this means that 1.4 x 1.428 = 2, the actual square root of 2 must be somewhere between 1.4 and 1.428. Taking the average of both, in this case 1.414, gives you a better approximation. Repeat, until you have the desired precision. This method is much faster than method (2); with every cycle, the amount of correct significant digits should be approximately twice the amount of the previous approximation.