Years ago I was taught how to calculate the exact square root of any number manually(no calculator).Now I just dont remember anything.

By the same analogy,how do you find the square root of a prime integer?

Thank you guys.

Tbone

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- Dec 12th 2009, 09:24 PMtbone1209Manual calculation of square roots
Years ago I was taught how to calculate the exact square root of any number manually(no calculator).Now I just dont remember anything.

By the same analogy,how do you find the square root of a prime integer?

Thank you guys.

Tbone - Dec 12th 2009, 09:39 PMProve It
Are you asking "How do you get the decimal approximation for the square root of a prime integer?"

Because you can't evaluate the square root of a prime integer exactly...

Babylonian - Dec 12th 2009, 09:50 PMBacterius
Nor can you evaluate the square root of any integer which is not the square of another integer.

It has been proved that if $\displaystyle n$ cannot be written $\displaystyle n = c^2$ with $\displaystyle c \in N$, then $\displaystyle \sqrt{n}$ is irrationnal (cannot be finitely written using decimals)

Little bonus : since $\displaystyle p$ is prime, it cannot be written $\displaystyle p = c^2$ with $\displaystyle c \in N$ (that would mean that p is composite and not prime), thus $\displaystyle \sqrt{p}$ is irrationnal.

Now you can approximate : take $\displaystyle \sqrt{7}$, for example.

You know that $\displaystyle 4 < 7 < 9$, thus $\displaystyle \sqrt{4} < \sqrt{7} < \sqrt{9}$

So $\displaystyle 2 < \sqrt{7} < 3$

Rince, reiterate (with closer bounds), and after some time you will get a pretty good approximation. - Dec 13th 2009, 10:19 AMtbone1209
Thanks guys!

Its nice to know. - Dec 13th 2009, 10:42 AMawkward
I think this may be what you have in mind.

Math Forum - Ask Dr. Math

It's how I was taught to do it, back in the Dark Ages (pre-calculator). - Dec 13th 2009, 01:00 PMtbone1209Back in the Dark Ages (pre-calculator).
That's exactly what I am looking for, Dr.Awkward.

"Dark Ages" I like that.I was at that critical period before;somehow thru the years I just could not recall that technique a 100%.I was just trying to show my kid in math that this could be done.Thanks again Dr.

I am a very new newbie with this forum.I read and gone through a lot of threads until I found this thread regarding this square root thing;not exactly what I was looking for and thats why my question was posted, with the same thread,for some help.There was no intention to break the rules for not starting a new thread and got a warning for it.I will remember now!

Above all,all you guys are great!I really appreciate the prompt response either way and thank you, Dr.Awkward.

Merry Christmas to you all

Tbone