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September 19th, 2018, 09:24 AM   #1
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Post squares

i.e. square of 26
n.n = (n-a).(n-a)+(n-a).(2a)+a.a
n = square of which we have to find {eg. 26}
a = any mnumber before the number whose square we have to find and whose
square is easy {e.g. 20,25}.
thus, putting the values,
n = 26
a = 20 {or25}
so,
(26).(26) = (26-20).(26-20)+(26-20).{2(20)}+(20).(20)
676 = (6).(6) + 6(40) +400
676 = 36+240+400
676 =676
[reason for taking 'a' as 20 ; because
we mostly know the square of 10* ]
whatsup me @9267500107

Last edited by skipjack; September 20th, 2018 at 10:32 AM.
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September 19th, 2018, 09:41 AM   #2
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Quote:
Originally Posted by keshri View Post
[SIZE="6"]i.e. square of 26
n.n = (n-a).(n-a)+(n-a).(2a)+a.a
n=sq][B]uare of which we have to find {eg. 26}
a=anynumber before the number who's square we have to find and who's
square is easy {eg. 20,25}.
thus, putting the values ,
n=26
a=20 {or25}
so ,
(26).(26)=(26-20).(26-20)+(26-20).{2(20)}+(20).(20)
676= (6).(6) + 6(40) +400
676= 36+240+400
676=676
[reason of taking 'a' as 20 ; because
we mostly know the square of 10* ]
whatsup me @9267500107
This is a confusing explication of a well known bit of mental arithmetic.

$26 = 20 + 6 \implies 26^2 = 20^2 + 2 * 20 * 6 + 6^2 = 400 + 240 + 36 = 676.$

Alternatively,

$26 = 30 - 4 \implies 26^2 = 900 - 240 + 16 = 900 - 300 + 60 + 16 = 676.$
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September 19th, 2018, 09:55 AM   #3
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Geezzzz....what does this mean:
[reason for taking 'a' as 20 ; because
we mostly know the square of 10* ]

And this:
whatsup me @9267500107

Last edited by skipjack; September 20th, 2018 at 10:33 AM.
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September 19th, 2018, 12:09 PM   #4
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Quote:
Originally Posted by Denis View Post
Geezzzz....what does this mean:
[reason for taking 'a' as 20 ; because
we mostly know the square of 10* ]

And this:
whatsup me @9267500107
I can only imagine that by '10*' he must mean multiples of 10. It's the only thing that makes sense. But, yeah, that wasn't clear.

As to the original question, I suspect that most of us use that basic technique when we have to calculate a square in our heads. In your example, I would have gone with 25. Even if you don't immediately know the square of 25, it's extremely simple to calculate and then your calculation ends up being: 625 + 50 + 1.

Last edited by skipjack; September 20th, 2018 at 10:34 AM.
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September 19th, 2018, 12:43 PM   #5
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Not so easy to manually calculate square root:

https://www.homeschoolmath.net/teach...-algorithm.php
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September 19th, 2018, 01:13 PM   #6
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Quote:
Originally Posted by Denis View Post
Not so easy to manually calculate square root:

https://www.homeschoolmath.net/teach...-algorithm.php
I seem to remember learning how to extract square roots by hand in the ninth grade and then learning logs and how to use a slide rule in tenth, which obviated the need to extract square roots.
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September 19th, 2018, 01:41 PM   #7
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...how to extract square roots...
...geezz Jeff, didn't know you wanted to be a dentist...
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September 19th, 2018, 02:55 PM   #8
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1$^2$ = 1
2$^2$ = 4
3$^2$ = 9
4$^2$ = 16
5$^2$ = 25
6$^2$ = 36
7$^2$ = 49
8$^2$ = 64
9$^2$ = 81
10$^2$ = 100
11$^2$ = 121
12$^2$ = 144
13$^2$ = 169
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September 19th, 2018, 04:25 PM   #9
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14^2 = 13^2 + 3^(2+2/2)
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September 20th, 2018, 03:34 AM   #10
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Smile pattern

You find something different in squares
like;
square of 1=1 [4-1=3]
square of 2=4 [9-4=5]
square of 3=9 [16-9=7]
square of 4=16 [25-16=9]
square of 5=25 [36-25=11]
square of 6=36 [49-36=13]
square of 7=49 [64-49=15]
the pattern plays like the odd once (1,3,5,7,9,11,1315,17,19.....)
this might help us in making formula for squares.

Last edited by skipjack; September 20th, 2018 at 10:35 AM.
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