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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: 8,139

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: 8,139

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: 8,139

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: 725

Do you need help with that?

Practice makes a man perfect.

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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