How to get the square root of 128?

Question

Please answer me!!

Answer 1

The square root of a number is just the number which when multiplied by itself gives the first number. So 2 is the square root of 4 because 2 * 2 = 4.

Start with the number you want to find the square root of. Let's use 12. There are three steps:

1. Guess
2. Divide
3. Average.

... and then just keep repeating steps 2 and 3.

First, start by guessing a square root value. It helps if your guess is a good one but it will work even if it is a terrible guess. We will guess that 2 is the square root of 12.

In step two, we divide 12 by our guess of 2 and we get 6.

In step three, we average 6 and 2: (6+2)/2 = 4

Now we repeat step two with the new guess of 4. So 12/4 = 3

Now average 4 and 3: (4+3)/2 = 3.5

Repeat step two: 12/3.5 = 3.43

Average: (3.5 + 3.43)/2 = 3.465

We could keep going forever, getting a better and better approximation but let's stop here to see how we are doing.

3.465 * 3.465 = 12.006225

That is quite close to 12.

Answer 2

Hi :

Here some websites that will help you:

http://www.qnet.fi/abehr/achim/calculato...
www.bright.net/~beeryde/ref/sq...

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


and there a five ways to do Square roots

If you are very good at addition,multiplying and division then use the Newton -Raphton method:

Gn= (SQRN/Gn+ Gn)/2

repeat using the new Gn each time for about ten times

Gn = guess number
SQRN = Number to square rooted

for example:

Square root of 26
Run # 1

Gn= 5

Gn= (26/5+ 5)/2

Gn= (5.2+5)/2

Gn= 10.2/2

Gn= 5.1

End of run #1

Run # 2

Gn = 5.1

Gn= (26/5.1+ 5.1)/2

Gn= (5.098039+5.1)/2

Gn= (10.198039)/2

Gn= 5.0990196

End of run #2

Do this for ten times and the Square root of 26
which appox equals 5.0990195


another way is to factor the Number being Square root

if you know the basic 1 to 12 roots

For example the square root of 8

8= 2*2*2

So (2*2)*2 = 4*2

and four square rooted is 2 So

Sqr(8) = 2 * Sqr(2)

the Square root of 2 = 1.14142135

So Sqr(8) appox = 2.82842713

#3 the School boy way see www.nist.gov/dads/HTML/squareR...

as to how to do that. Which is the best method to do them. If you can't do the above or below

# 4 ) the Bablyon method

Using S=(x+y)^2 ( y being the the closes square of the number without going over it see the example

S= x^2+2xy+y^2

S-y^2 = x^2 + 2xy
S-y^2 = x(x+2y)

S-y^2
------- = x(x+2y)/(x+2y)
(x+2y)

S-y^2
------ = x
(x+2y)

For example the Square root of 5

5= (x+2)^2 = (x+2)(x+2)

5= (x^2 +4x+4) ( y=2 here so 2*2 = 4)

5-4=x^2+4x+4-4

1= x^2+4x

1= x(x+4)

1/(x+4)=x(x+4)/(x+4)

1/(x+4) = x

Run 1

1/(1+4)= x

1/5= x

x=.2

run 2

1/(.2+4)= x

1/4.2= x

x= 0.2359550

run 3

1/(0.2359550+4) = x

x= 1/ 4.2359550

x = 0.235955

run 4

1/(0.235955+4) = x

1/(4.2359550) = x

0.236074 =x

run 5

1/(.236074+4) = x

1/(4.236074) =x


4.236074= x

0.2360676 =x

End of run 5

(2+x)^2 = 5

x = 0.2360676

So 2.2360676 is the square root of five

2.2360676 ^2 = 4.99999 close enough for government work

# 5 memerize the logarithm table one thru 1000

and squares and square roots and cube cube roots and any other powers or roots is a breeze

Hope this helps

Ps: #6 do
log(N)/2
or ln(N)

then divide either one by 2
and take it antilog
and you will have your square root

for example :

Log(128) = y

2.107209970= y { I rounded every number to 9 decimal places here }

then divide it by 2 like so:
2.107209970 /2 = 1.053604985

Now take the antilog like so:

10^1.053604985 = 11.3137085

proof:

11.3137085 * 11.3137085 = 128

128. = 128 they equal, Good

Answer 3

I don't think you can get the square root easily, if it helps the value is 11.31 (2 d.p.). You can follow the logic of an earlier answer: root(128) = root(2*64) = root(2)*root(64) = 8*root(2) The square root of a number is the value which when multiplied with itself gives the number. Exact solutions are quite easy to calculate, such as sq. root of 100 (10) or 144 (12). When the root of an integer is not a whole number it is known as an irrational number - it cannot be represented as an exact fraction. Oh, and Gambit is a total ********. Actually Gambit, I'm in a profession which actually makes a difference to the world with original ideas and research. What do you do? When you're not being an ******** that is. How do you expect people to learn if they don't know the answers. The questioner isn't asking for a number to write on a piece of paper to hand in to her teacher, she is asking for an explanation to aid her learning. Not all the answers are in the school books. Do you even know what an imaginary number is? People like YOU, who think they are the last stand in the fight against the youth of today are the people who will be the proverbial nail in the coffin for "this country", the almighty USofA? Jackass.

Answer 4

Uck, I hate square roots too! An even square root is two numbers mulitiplied by itself that equals the the square root. For example the square root of 16 is 4. . . because 4 times 4 is 16. In this case there are not 2 numbers that can be multiplied to equal 128. So the answer will be 11.3--- good luck with them!

Answer 5

It is eight times the square root of two. Just factor 128.

128 = 4 x 4 x 2 x 2 x 2 =(4 x 2) x (4 x 2) x 2 = 8 x 8 x 2

Answer 6

you could factr it and get

sqrt(128) = sqrt(64)sqrt(8)
= 8 sqrt(2) to be exact

but for an approximation you must use a linearization of sqrt(x) near 128. (use a= 121)

L(x)=f(a) + f'(a)(x-a)

where f(x) = sqrt(x)

so sqrt(128) = (about) sqrt(121) + 1/2sqrt(121) * (128-121)
=11 +1/22*7
=11 +7/22 = 219/22

lets compare
219/22 = 11.3181812 my approximation
sqrt(128) = 11.3137085 from calculator

very close =)

Answer 7

128 = 2^7 is not a square but (2^7)^0.5 =11.33

Answer 8

128 = 2^7 is not a square but (2^7)^0.5 =11.33

Answer 9

11.313708