
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 = (na).(na)+(na).(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) = (2620).(2620)+(2620).{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  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
$26 = 20 + 6 \implies 26^2 = 20^2 + 2 * 20 * 6 + 6^2 = 400 + 240 + 36 = 676.$ 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  
Newbie Joined: Jul 2018 From: Georgia Posts: 28 Thanks: 7  Quote:
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  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
 
September 19th, 2018, 12:41 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,415 Thanks: 1025  
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 
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) 
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 [41=3] square of 2=4 [94=5] square of 3=9 [169=7] square of 4=16 [2516=9] square of 5=25 [3625=11] square of 6=36 [4936=13] square of 7=49 [6449=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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