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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

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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: 14,415 Thanks: 1025 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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 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: 14,415 Thanks: 1025 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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 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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 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: 7,935 Thanks: 1129 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: 14,415 Thanks: 1025 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. Tags squares Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post 3uler Calculus 22 August 17th, 2014 03:55 AM Hoempa Math Events 2 December 6th, 2013 01:12 AM ungeheuer Algebra 3 July 3rd, 2013 12:51 PM mathkid182 Linear Algebra 2 May 1st, 2013 03:39 PM WillingSponge Number Theory 5 July 9th, 2010 06:52 AM

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