Square root of 2? without help of calculator.?

Question

i want to know the complete steps of finding square root of any number withot the help of calculator.

Answer 1

to get tehe square root do the follwoing
1st divide digits of the number into pairs
for example

if the number is 48596
make is
04 85 96
& start from the left pairs
04 , find out a number its square equals to or just less than 4 ---> it is 2

then subtract this square from the left pairs of number
04 85 96
04
------
00 85 96 ----------> until now the result contains 2
85 96

then the rest we will use the following formula a(a+20 r)
where r is the result the we get from the start till the previous step
& 'a' is an integer number 0 <=a <=9
in this formula a(a+20 r) a must be less than the next pairs (with the remain if any)
so here we need the value of 'a' where a(a+20*2)<= 85
a(a+40)<=85
if a 0--->0 1--->41 2--->84 3----> 129
so it is 2
so put it to the right side of the result (the result will be (22)
subract
85 96
84
--------
01 96
then use the formula again
find a where a(a+20*22)<196
a(a+440)<196
if a 0--->0 1--->441 >196
so a here will be 0
& the reault will be (220)
& the remain is 196
if u want to continue with fraactions
add 00 to the right & a decimal point in the result
so
19600
find a where a(a+20*220)<19600
it will be 4 4(4+4400)= 17616
put 4 in the result (220.4)
subtract

19600
17616
--------
1984
add 00
198400
and so on
----------------------
try to get the square root of 2 with this method
the start is
02 ---->a=1
01
-----(subtract)
01 00 (result 1. )
a(a+20*1)<100 a=4--->96
subtract
1 00
0 96
-----
4 00 ------->result (1.4)
and so on

Answer 2

Well Today is your lucky day if you dont want to use the cal use your brain lets start with let x = √2 then square both sides gives us x^2 = 2 right take 2 to the left hand side gives us x^2 -2 = 0 >>> which gives us a graph of y= x^2 -2 ...
Now the tricky part use this FORMULA A - F(a)/F'(a) where your equation is f(a) x^2 -2 .. take a approximation of say 1.8

then do this 1.8 - F(1.8) divided by F'(1.8) remember F'(a) is the dy/dx ok ill just give you the final step so you just need o substute in your calcultor and you got he best approx of V2 ok


1.8 - 1.24/ 3.6 should give you close to 1.4 ive got this another method which is a pattern if you need it pm me on [e-mail] but the method i showed you works for all square roots of all numbers thanks

Answer 3

Sense they are both square roots, all you have to do is multiply the numbers and keep t as a square root. Sooooo. Sqrt of 116 Times Sqrt of 2 = sqrt of 232 ( because 116 times 2 = 232) another example... What is the sqrt of 3 times the square root of 5? Well, That is the sqrt of 15... Same with addition, subtraction and multiplication... EXAMLES: sqrt of 5+sqrt of 3+ sqrt of 8 sqrt of 5 - sqrt of 3 = sqrt of 2 sqrt of 10 divided by sqrt of 5 = sqrt of 2 hope I helped! :) -Andrew

Answer 4

Newton's Approximation:
each iteration is more accurate than the last, with n being the argument of the sqrt function
x(k+1) = 0.5*(x(k) + n/x(k)) with x(0) = 1
for example, when n=2, x(0...4)=
1
1.5
1.41667
1.41422
1.41421 ~= sqrt(2)

Without a calculator, just guess and check each decimal place, approximately dividing your remaining range by two if possible:
1^2 = 1 (>)
2^2 = 4 (<)
::1 1.5^2 = 2.25 (<)
::1 1.3^2 = 1.69 (>)
::1.3 1.4^2 = 1.96 (>)
::1.4 ...

Answer 5

all you have to do is think of a number that multiplies by itself and the # u get is its square. So the square root of the # is the orginal # you multiplied. Say u use the # 3. 3 * 3 is 9. So the square root of 9 is 3. Not hard.

Answer 6

(radical)2
add a 0 in front of the 2
(radical)02
now theres a pair behind the decimal
so estimate the square root of 02
which is approx. 1.4
think: 1.4 x 1.4 = 1.96 (2)

Answer 7

square root of 2= 1.4141

Answer 8

I don't know about the exact way of doing this, but I know that sqrt(2) has to be a little more than 1 but a little less than sqrt(3) which is less than sqrt(4) = 2, so it should be about 1.4

Answer 9

Someone already mentioned using Newton's Method.

Other ways to approximate it are by using the Secant Method or by using the Taylor Series.

Answer 10

Then check the site in the source.