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 September 19th, 2018, 08:24 AM #1 Newbie   Joined: Sep 2018 From: india Posts: 2 Thanks: 0 Math Focus: all 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 09:32 AM.
September 19th, 2018, 08:41 AM   #2
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Quote:
 Originally Posted by keshri [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,

$26 = 30 - 4 \implies 26^2 = 900 - 240 + 16 = 900 - 300 + 60 + 16 = 676.$

 September 19th, 2018, 08:55 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,302 Thanks: 935 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 09:33 AM.
September 19th, 2018, 11:09 AM   #4
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Quote:
 Originally Posted by Denis 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 09:34 AM.

 September 19th, 2018, 11:43 AM #5 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,302 Thanks: 935 Not so easy to manually calculate square root: https://www.homeschoolmath.net/teach...-algorithm.php
September 19th, 2018, 12:13 PM   #6
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Quote:
 Originally Posted by Denis 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.

September 19th, 2018, 12:41 PM   #7
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Quote:
 Originally Posted by JeffM1 ...how to extract square roots...
...geezz Jeff, didn't know you wanted to be a dentist...

 September 19th, 2018, 01:55 PM #8 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond 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 Thanks from Denis
 September 19th, 2018, 03:25 PM #9 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,302 Thanks: 935 14^2 = 13^2 + 3^(2+2/2) Thanks from greg1313
 September 20th, 2018, 02:34 AM #10 Newbie   Joined: Sep 2018 From: india Posts: 2 Thanks: 0 Math Focus: all 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 09:35 AM.

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