# Manual calculation of square roots

• Dec 12th 2009, 09:24 PM
tbone1209
Manual 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 PM
Prove It
Quote:

Originally Posted by tbone1209
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

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 PM
Bacterius
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 AM
tbone1209
Thanks guys!
Its nice to know.
• Dec 13th 2009, 10:42 AM
awkward
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 PM
tbone1209
Back 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