Is there a way to calculate square root?

Answer 1

There are at least two ways to calculate square roots:

1) Find the log (to any base) of the number and find the antilog (to the same base) of the log divided by 2.

2) Use a kind of "long" division:

a) split the number into pairs of digits starting at the decimal point (to the left the last pair may only have a single digit - doesn't matter; to the right if the last pair is a single digit add a zero to make a pair; and write a decimal point in the answer above the decimal point in the number; extra pairs of zeros can be added after the decimal point to get to the desired degree of accuracy;

b) Now do a "long" division by starting with the left most pair and finding the largest number which when squared is less than or equal to it; write this number in the answer above the first pair

c) write the number squared under the first pair and subtract it;

d) bring down the next pair (as in a long division) (to create the current "dividend"

e) double the whole answer so far (ignoring the decimal point) and multiply it by 10 (ie multiply it by 20) to create the "divisor"

f) Now the hard part: find a digit to put in the ones place so that when the divisor is multiplied by this digit it is the largest possible number less than or equal to the current dividend.

g) multiply the divisor with the ones digit replaced by the digit just found, write it under the current dividend and subtract

h) if all the digit pairs of the number have been used up and the last subtraction is zero the square root has been found

i) otherwise, if the required degree of accuracy has not yet been reached, repeat from step d.

Answer 2

Obviously; otherwise calculators couldn't do it. I strongly suggest you use a calculator, but that's probably not what you wanted to know.If you ask, say, for the square root of 2, you want a number which, when squared, gives you 2.

Therefore, the obvious method is to try out squaring different numbers. For example: the square of 1 is 1, the square of 2 is 4; therefore, the square root must be somewhere between 1 and 2. You can continue experimenting, to get more decimals.

Here is a faster method: First, get a rough estimate. See above: the square root must be between 1 and 2. Divide 2 (the number I want the square root of) by 1. The result is 2. That means that 1 x 2 = 2. The real square root should be close to the average of these two factors.

Repeat, by dividing 2 by 1.5. The result is 1.333. Once again, 1.5 x 1.333 = 2; take the average of the two factors for the next approximation - that would be about 1.4.

Continue, to get more decimals. With each step, the number of significant digits in the result will double, more or less.