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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 648

Hi;

How to take square root of number like 0.2, 0.34,0.23455 etc without calculator

Sqrt of 0.2 is ???

0.707 multiple b 0.707

MZk

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,084

hi Zeeshan 01

If you google "square root without a calculator" you'll find loads of sites offering methods. They all need some arithmetic however. How's your long division?

A method I rather like is this:

Let's say the number is N. Take a guess for the square root, say x, and do N÷x = y.

If x was too small then y will be too big and vice versa. So work out (x+y)/2 and make this your next guess. This 'homes in' on the root quite quickly.

eg. N=50 x = 7

y = 50/7 = 7.14.....

(x+y)/2 =7.0714...

new x = 7.0714....

new y = 7.070707

new(x+y)/2 = 7.071068

This is accurate to 5 decimal places.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 648

bob wrote:

Hows your long division?

Pretty Good

*Last edited by Zeeshan 01 (2017-05-31 06:00:23)*

MZk

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 648

Sqrt of 0.2 is ???

Can you put this info in your method??

MZk

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,084

here we go:

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 648

??? N is 0.2 and how x is 1 and y is 0.2

MZk

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,084

Zeeshan 01 wrote:

N is 0.2 and how x is 1 and y is 0.2

You asked for

Sqrt of 0.2 is ???

So that makes N=0.2

x is a guess. It can be any number. If you chose a value close to the correct answer, then you'll get to an accurate answer more quickly. But any number will work so I chose x = 1.

Then you calculate y using the formula y = N/x= 0.2/1 = 0.2

Then you calculate the mean average of x and y = (1+0.2)/2 = 1.2/2 = 0.6

That becomes the new x. Repeat until x and y are so close to each other that (x+y)/2 gives the same result. That's the square root.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 648

Hmm

MZk

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 648

You know proportions direct and indirect??

MZk

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 692

Do you need help with that?

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 648

So work out (x+y)/2 and make this your next guess

How x become (x+y)divde by 2

MZk

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 648

How x become (x+y)divde by 2

MZk

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