How do you compute the square root without using calculator?

Answer 1

There are several methods. An easy one is trial-and-error: keep finding the square of several numbers; if the result is too high, choose a lower number, if it is too low, choose a higher number.

Repeated division works much faster. Let's assume you want the square root of 2. Your initial estimate for the square root is 1. You divide 2 / 1 = 2. Take the average of the last two numbers, 1.5. This is the next estimate. Repeat: Divide 2 / 1.5 = 1.33... The average of the last two numbers is about 1.4. Repeat, using this as your next estimate. The number of significant figures doubles with each repetition.