How do You do square root?

Answer 1

If you mean how to calculate square roots "from scratch", here's method devised by the ancent Babylonians. (Nowadays it's ususally referred to as a special case of something called Newton's method, but I like to give credit to the Babylonians!)

say you want the square root of 20.

Make a reasonable first guess. say 4.

Now divide 20 by 4.

Before doing this, think about what might happen:

If 4 is the correct square root (it isn't) then the answer you get after dividing will be 4.

If 4 is an underestimate of the square root, then the answer you get will be an overestimate.

If 4 is an overestimate of the square root, then the answer will be an underestimate.

(because 4 x answer = 20)

Now 20/4 = 5. ( So 4 is too small and 5 is too big)

Take the average of 4 and 5 to be your next guess.

this is 4.5.
20/4.5 = 4.444444444444444444

Now so 4.5 is too big and 4.44444444444444 is too small.

Average them, to get 4.72222222222222222222
20/4.72222222222222 = 4.4720496

so the root is between 4.722222222222 and 4.4720496.

Average them to get 4.47213595503

20/4.47213595503 = 4.47213595417

You can see that the last two results agree to several places.

So the square root of 20 is about 4.472136

Answer 2

I assume you're trying to do this by hand rather than using a calculator.

The easiest way, conceptually to do it is this. Pick a number close to what you think the square root is. So if you're trying to determine the square root of 5, start with 2. Divide 5 by 2, yielding 2.5 as your answer. Since that isn't the square root, take the number exactly halfway between 2 and 2.5, which is 2.25. Divide 5 by 2.25 which gives 2.2222222 (repeating 2s)

Wow, two steps and we're already within .03 of one another...

Take the number halfway in between those two, which would be 2.235 (approximately). Divide 2.235 by 5..this yields 2.2371364... How precise do you need the number? Take the number halfway in between these two, which is 2.236. Divide that by 5, which gives 2.23615957, now we're within 1/10,000th of the each other. Just keep doing this until you get to the precision you need. You'll never get it perfectly, since all non-integer square roots are irrational numbers, that is to say, non-terminating, non-repeating decimals.

Answer 3

It would take too long to explain how to calculate a square root by hand, it can be done. Calculators have made math much less work for us. "Trig" functions are just one example of that! Fire Fox has a detailed explanation how to do so. Type into browser "square root calculation! Sorry, there is no other quick way to explain.

Answer 4

Use you calculator, or
Do it manually. Look up how to extract the square root of a number on the internet.

Answer 5

only iterative process... try and fail then try again until you reach a good result...