How do you find the square root of a number with a regular calculator?

Answer 1

Type in the number and press the square root button which looks like this: √

Alternately, you can type in X1/2 and you'll get the same thing.

If you only have a four-function calculator, there are a couple of methods. One is simply trial-and-error: make a guess, square it (multiply it by itself), see if it is too large or too small and adjust your guess. It's accurate, but takes several iterations.

Another technique is called the "Babylonian Method". It is similar, but it converges on an answer more quickly. You make a guess, divide the number (that you want to find the square root of) by your guess, and then take the average of that result and your guess. That becomes your next guess. For example, if you want to find the square root of 60, you know that 8x8 is 64 so that's a good starting guess:

guess: 8.00000, divide: 60/8.00000 = 7.50000, average = 7.75000

guess: 7.75000, divide: 60/7.75000 = 7.74194, average = 7.74597

guess: 7.74597, divide: 60/7.74597 = 7.74597, (same as the guess, to five places)

It's very easy if your calculator has a memory register where you can store the guess. All you have to do is divide and average, divide and average...