calculate the square root without using root button in a caculator?

Question

hi
my qs is pretty simple

how can i calculate the square root of a number without actually using the root buttoin in my calculator ?

give me answers step by step ;)

cheers

Ankiee

NO PEN AND PAPER ALLOWED

think without ink ;)

Answer 1

Hi:

I know of six ways to find a square root of a number:

1) Take the logarithm of number and divided by 2 take the result and take the Antilog

2) Use the School boy method of extracting a square root see this website for how :

www.nist.gov/dads/HTML/squareR...

3) Use the following method ( example on the bottom of page ):

(N/gn+gn)/2= gn

N= number to be Square root
gn = Guess number or Square root

repeat this for about about 5 to 10 times ( see example)

4) Use trail and error by running a number value and Square it

5) Graph and interpolarite it

6) Look it up in a Mathematical hanbook of tables and formulas and look under Square & square roots tables.

------------------------------...



Example:

The square root of 27:

(27/5+5)/2= gn


(5.4+5)/2 = gn

10.4/2= gn

5.2 =gn
end of run 01

(27/5.2 + 5.2)/2= gn

(5 + 5.2)/2 = gn

10.2/2= gn

5.1= gn

end of run 02

((27/5.1)+ 5.1) /2= gn

(5.294117647+5.1)/2 = gn

10.394117647/2 = gn

5.197058823 = gn

End of run 03

(27/ 5.197058823) + 5.197058823 )/2 = gn

(5.195246179+ 5.197058823 )/ 2 = gn

10.392305003/2 = gn

5.196152501 = gn

End of run 04

((27/5.196152501)+ 5.196152501)/2 = gn

(5.196152343+5.196152501)/2 = gn

10.392304844/2 = gn

5.196152422= gn

End of run 05

((27/ 5.196152422) + 5.196152422 )/2 = gn

(5.196152422 + 5.196152422 ) /2 = gn

5.196152422 = gn

End of run 06

Square root of 27 appoximatily = 5.196152422 ( accurate to 9 decimal places.)

Source(s):

www.nist.gov/dads/HTML/squareR...

www.du.edu/~jcalvert/math/sqrt...

mathforum.org/library/drmath/v...

Answer 2

Take a guess at the square root--anything reasonable will do. You can pick something unreasonable, too, just not zero: it just takes longer. Call your guess A. Your number, I shall name N.

Compute: B=N/A

Compute: C=(A+B)/2

Now, let us assume A>B for the purposes of argument. If it's not, just swap 'em so it's true...

ANYHOW,

Compute C' = N/C

If C > C' then A = C

If C = C' then you've got your square root, right there!

If C < C' then B = C

Now, recompute C = (A+B)/2

GO back and recompute C' and do this all over again.

Eventually, you'll reach a point where C-C' is smaller than your calculator can handle; you're essentially there.

Notice that the distance between A & B pretty much drops by half every time you run through this cycle...

This is VERY fast: in 10 repetitions, you're within 1 part in 1000; in 20, 1 in 1000000; in 30, 1 in 1000000000...

Answer 3

Assuming you have a scientific calculater, you can use the power key, usually ^ or y^x where the power is 0.5. So, 9^0.5=3, same as the square root.

If you don't have a scientific calculator you need to go through it manually, basically, guessing and testing is faster as you should have some indication given the size of the number.

Answer 4

x is the square root of x^2. So the square root of a number is a number that if multiplied by itself is the product of the whole number. Example 2 is the square root of 4. 2x2=4.
8 is the square root of 64. 8x8=64. etc.
So you must find a number that if multiplied by itself is the answer.

Answer 5

You may consider it cheating, but...

Though you specified that using the square-root button is not allowed, you did not say that using the exponential (x^y) button is not. So simply enter your original number, press the exponential button, enter 0.5, and press equals. Easy! ^.^

Of course, if you meant only using the "basic" mathematical functions ( * / + - = ), then see some of the answers above for the series approximation method.

Answer 6

I teach a square root algorithm, but it requires pen and paper. It's similar to long division, though you have to use two digits at a time (counting from the decimal point in either direction). Kinda complicated to put it to words here, though. :-(

Answer 7

prime factorization. Example: sqrt(81)= 3*3*3*3 = 3^2*3^2= 9

Answer 8

Press a number
Press x^y
Press .5
Press enter

don't believe me, just try it.

Answer 9

you shud know the pairing up of digits way..the old way

Answer 10

break it down to primes