How do you fine square root of 712 with out a calculator?

Answer 1

The answer is: 26.6833281283

Answer: To calculate the square root of any number without a calculator is a lot of work - not really worth the trouble. Anyway, here is one method. Make an initial estimate for the square root; since 20 squared is 400 and 30 squared is 900, it must be somewhere in between. Let's say we take 20 as our initial guess. Try dividing 712 / 20. The result is 35.6. Now, since 20 x 35.6 = 712, the real square root must be somewhere between those two factors. You might take the average, but for now I'll use 30 as an approximation.

Repeat: 712 / 30 = 23.73. Once again, the real square root is somewhere between 30 and 23.73. The average (rounded to the nearest integer) is 27.

Repeat with this number: 712 / 27 = 26.37. Taking the average of 27 and 26.37, you get 26.69.

Repeat, using 26.69 as the new estimate for the square root. With every step, the number of significant digits in the estimation should more or less double.