Question

Can someone explain to me, in lamens terms (Pretend I am Extremely Dumb) how to calculate the square root of a large number, with four or five digits, without a calculator? Say The Sqrt(50989)

Answer 1

*Layman's Terms then, if you please.

Answer 2

Still don't get it, at all -_-

Answer 3

50989 100 is a perfect square and so you can start from the RIGHT and skip every two digits and you will be left with 5. Estimate sqrt(5). The sqrt(50989) will be in the vicinity of 2*10*10

Answer 4

Why would you start with the idea that 100 is a perfect square?

Answer 5

Interesting that you'd pick such a large prime number...

Answer 6

Let's say I did that on purpose.

Answer 7

Let us say the number is 40,000
40,000 = 4 * 100 * 100
square root = 2 * 10 * 10 = 200

Answer 8

Alright. 40, 000 = 4 * 100 * 100, I'm with you there.

Answer 9

50989 is approx 5 * 100 * 100
so we get the ballpark estimate of sqrt(5) * 10 * 10 approx 200.
Now we can refine it by trial and error.

Answer 10

You know what, this is so hard that I'm going to stick with it until I can do these in my head. By hand first.

Answer 11

As in sqrt(5 * 100 * 100) Ok, cool, I get that

Answer 12

I don't want trial and error, I want an exact method! Lol!

Answer 13

Another way, assuming you were given the square root of a number close to \(\sqrt{50989}\approx 225.807\), such as \(\sqrt{50625}=225\), you can use the linear approximation technique to estimate the first square root.

Take the function \(f(x)=\sqrt x\), then
\[f(50989)\approx f(50625)+f'(50625)(50989-50625)\]

Answer 14

You just mind grenaded me Siths

Answer 15

Gimme a min to look at this

Answer 16

If you haven't seen anything about the linear approx. yet: http://tutorial.math.lamar.edu/Classes/CalcI/LinearApproximations.aspx

Answer 17

I sure haven't. Let me do that tutorial. I'll be right back.

Answer 18

You can also look up Newton-Raphson or just Newton method. But it is a successive approximation method.

Answer 19

Wait, isn't the f'(x) when talking about \[f(x) = \sqrt[3]{x} \] equal to x^3?

Answer 20

I haven't taken any calculus, is that an issue, or can I still get this?

Answer 21

It is cube root

Answer 22

Well thanks for the help anyways. I'll figure it out.

Answer 23

You will have to know how to find the derivative of a function which is taught in calculus. But if all you are interested in is the square root function you can just memorize the derivative.

Answer 24

Nah, I'm interested in learning Calculus much more than I am about learning this square root by hand operation. I need to be in the equivalent of Calculus 3 in less than 6 months. Then I have about 8 years of college ahead of me lol