## Square Root (2004 html file)

December 10th, 2020**Manual Calculation of Square Roots**

**n****^**

^{0.5} (n is a real number)

You can, and hopefully will, try this process using any number and then check the result

otherwise. The 'reasoning' behind this method is available - **Ref: END NOTES.**

First the number to be 'rooted' is formatted into

digit pairs either side of the decimal point, adding pairs of

zeros if further accuracy is required. For example : A solution

to three decimal point requires four pairs of digitits after the

decimal point.

To find the square root of **623.45**

to **2dps** we would format the 'subject number' as

follows in row 1. of the following table, then process as per the

remaining rows.

>

Row |
ses | Result |
Use |
| ||

1. | Format Subject Number (623.45) and place the decimal point. |
6'23.45'00'00 | Place formated number as in long division |
. |
||

6'23.45'00'00 |
||||||

2. | Find highest integer that when squared is <= the first 'pair' of digits. |
2 | Place result above it's digit pair |
2 . |
||

2 | 6'23.45'00'00 |
|||||

3. | Multiply the integer above by the result | 2 x2 = 4 | Subtract the result from the first 'pair' of digits. |
2 . |
||

2 | 6'23.45'00'0042 |
|||||

4. | Bring down the next pair of digits. | 23 | Thie new subject is 223 | 2 . |
||

2 | 6'23.45'00'0042'23 |
|||||

5. | Multiply the existing result (2) by 2 | 2 x 2 = 4 | Place it to the left with space for a second digit |
2 . |
||

2 4_ |
6'23.45'00'0042'23 |
|||||

6. | Find the largest 'a' where ((fourty+a) x a) <= the subject |
a=4 44 x 4 = 172 |
Place the '4' above the second pair of digits |
2 4. |
||

2 44 |
6'23.45'00'0042'23 |
|||||

7. | Multiply the integer above by the result | 176 | Subtract the result from the new subject (223) |
2 4. |
||

2 44 |
6'23.45'00'0042'23 471'76 |
|||||

8. | Bring down the next pair of digits. | 45 | 2 4. |
|||

2 44 |
6'23.45'00'0042'231'76 47'45 |
|||||

9. | Multiply the existing result (24) by 2 | 48 | Place it to the left withspace for another digit |
2 4. |
||

2 |
6'23.45'00'0042'231'76 47'45 |
|||||

10. | Find the largest 'a' where ((fourhundred and eighty+a) x a) is <= the subject |
a=9 489 x 9 =4401 |
Place the 'a' above the next pair of digits |
2 4. 9 |
||

2 44 48_ |
6'23.45'00'0042'231'76 47'45 |
|||||

11. | Multiply the integer 'a' by the result | 4401 | Subtract the result from the new subject (4745) |
2 4. 9 |
||

2 |
6'23.45'00'0042'231'76 47'4544'013'44 |
|||||

12. | Bring down the next 2 digits. | 00 | Subtract the result from the new subject (4745) |
2 4. 9 |
||

2 |
6'23.45'00'0042'231'76 47'4544'013'44'00 |
|||||

13. | Proceed as per 9 onwards. Then 10. Double the 'answer so far' Find the largest 'a' where ((four-thousand nine-hundred and eighty+a) x a) <= the new subject (34400) |
2 x 249 = 498 |
2 4. 9 |
|||

2 44 489 498_ |
6'23.45'00'0042'231'76 47'4544'013'44'00 |
|||||

END NOTES :- Ok that's the general idea. Although I have known this process for over 40 years, it is only in the last few weeks (2004) that I discovered how the above process worked during my latest attempt to discover a method to find the third root of a number. All the best - Roger Lovejoy - 7th November, 2004 |

## Math: Sqaure & Cube Root

December 10th, 2020Square root

Any number can be seen as the sum or product of other numbers. For example as 25 is the sum of 16 and 9 then (16 + 9) x (16 + 9) can be used in the following fashion:

25² can be written as (16 + 9)²

Now (16 + 9) x (16 + 9) can be expanded to 16x16 + 16x9 +16x9 + 9x9 which provides the basic formula that c²=(a+b)² = a² + 2ab + b²

It is from this later expansion that the square root of a number can be calculated manually as follows:

As we know the answer to the simple value of 25² is 625 then I will root the 625 as follows, the method is to find suitable values for a and b.

The number to operated on is 625 and this number is placed similarly to a long division example under a bracket and horizontal line

______

) 625

Noting that a square root of a number must be half the digits of the number in question the number 625 is separated by a space, every two digits from the decimal point. So we write it as

___________

) 6 25.00 00

The subsequent pairs of zero are only shown as the layout where the answer may require a decimal value, a pair of zeros for each decimal place to be calculated.

The first job is to find the highest number (single digit) than when squared is less than 6, in this case it is 2. The 2 is placed above the 6

_2__________

) 6 25.00 00

The digit 2 is in effect the a in the algebraic formula. This number is squared to 4 to represent the a² and the value is subtracted from the 6

_2__________

2 ) 6 25.00 00

4

The next part is to find 2ab and in similar fashion.

First take away the value of the square 4 from 6 and bring down the next pair of digits

_2__________

2 ) 6 25.00 00

4

4 25

The a is multiplied by 2 > 2a and placed outside as follows:

_2__________

2 ) 6 25.00 00

4

4_

## Zero to Infinity

December 10th, 2020Saying nothing can be compared to zero or even that everthing can be related to infinity creates a problem in use of the concepts, however.

1. Being absent is a bit like zero, the option of not existing. is that an option if awareness is a body ~ Buddha

2. The option of infinite existence seems more desirable and possible as it does not equate to not having a body and an awareness., Saturn, Moon, Earth, Jupiter Mars and the Sun

3. Some middle way between zero and infinity. Seems the as of organised religion, laws, politics,

4. Negative Infinity, but now we have the notion that zero is the core.

## An Argument on Moral

December 10th, 2020Words that do not denote a corporate form, like 'apple' almost always have a polarised sense in that there is an opposite in this case, immoral.

A clear definition of any word is an impossibility as communication and language is relative, to experience and position. However moral seems to indicate other polarised ideas such as 'good'

The application of a word may help clarify an inherent meaning although by no means is it absolute in expression or reception.

It may be that the killing of another human is immoral and if that be the case decisions that conclude the better/lesser of two evils, i.e. whether to kill one entity to support or save another seems inherently immoral too. What most people act upon is that, which is often the preferred outcome of immoral action. Morality is therefore not a question of lesser of two evils but how to avoid the killing.

Death in itself is not immoral and is the only guaranteed outcome of being a consumer not matter the sum of an individuals attempts to prolong their own existenmce at the expense of others. Death is the bonly right. ie.e the only guaranteed benefit, althogh few see it as such.

Moral arguments must be confined to ones that do not require acts of consumption. An act of sacrifice may indicate an acjknowledgement of moral value but depriving oneslef is no more moral that depriving another.

The worldly solution so soughgt after by mystics is to forgoe consumption without sacrifice. Mediation on life as a consumer only furthers the temproral body at the expense of the soul.

## Where's the pain?

December 9th, 2020I have suffered and been the transferrer of pain, radiant and transparent. It would seem there \is no absolution no way of bein absent, yet I dwell through time maybe trying to dilute the feeling. I wish I were strong enough to feel but am inclined to a destiny taht will deprive me of awareness of those times the suffering endured.

It's here, dare I access it, will I founder it a time of pain a time of desire, a time of my own. It is not something I wish to share so I struggle to free the mind from time where pain is just a lack of feeling what eternally exists.